the measure theoretic identity underlying transient fluctuation theorems we prove a measure theoretic identity that underlies all transient fluctuation theorems tfts for entropy production and dissipated work in inhomogeneous deterministic and stochastic processes including those of evans and searles crooks and seifert the identity is used to deduce a tautological physical interpretation of tfts in terms of the arrow of time and its generality reveals that the self inverse nature of the various trajectory and process transformations historically relied upon to prove tfts while necessary for these theorems from a physical standpoint it is however not necessary from a mathematical one the moment generating functions of thermodynamic variables appearing in the identity are shown to converge in general only in a vertical strip in the complex plane with the consequence that a tft that holds over arbitrary timescales may fail to give rise to an asymptotic fluctuation theorem for any possible speed of the corresponding large deviation principle the case of strongly biased birth death chains is presented to illustrate this phenomenon we also discuss insights obtained from our measure theoretic formalism into the results of saha et al on the breakdown of tfts for driven brownian particles

bit error rate of binary and quaternary dpsk signals with multiple differential feedback detection a differentially coherent detection scheme with improved bit error rate ber performance is presented for differentially encoded binary and quaternary phase shift keying psk modulation the improvement is based on using l symbol detectors with delays of 1 2 l symbol periods and on feeding back detected psk symbols exact formulas for the bit error probability are derived for the case that correct symbols are fed back the effect of symbol errors in the feedback path on the ber is determined by computer simulations

fluctuation theorems and atypical trajectories in this work we have studied simple models that can be solved analytically to illustrate various fluctuation theorems these fluctuation theorems provide symmetries individually to the distributions of physical quantities such as the classical work wc thermodynamic work w total entropy stot and dissipated heat q when the system is driven arbitrarily out of equilibrium all these quantities can be defined for individual trajectories we have studied the number of trajectories which exhibit behaviour unexpected at the macroscopic level as the time of observation increases the fraction of such atypical trajectories decreases as expected at the macroscale the distributions for the thermodynamic work and entropy production in nonlinear models may exhibit a peak most probable value in the atypical regime without violating the expected average behaviour however dissipated heat and classical work exhibit a peak in the regime of typical behaviour only

asymmetry of the work probability distribution we show both analytically and numerically that for a nonlinear system making a transition from one equilibrium state to another under the action of an external time dependent force the work probability distribution is in general asymmetric even if the evolution dynamics has a symmetry

experimental study of the fluctuation theorem in a nonequilibrium steady state the fluctuation theorem ft quantifies the probability of second law violations in small systems over short time scales while this theorem has been experimentally demonstrated for systems that are perturbed from an initial equilibrium state there are a number of studies suggesting that the theorem applies asymptotically in the long time limit to systems in a nonequilibrium steady state the asymptotic application of the ft to such nonequilibrium steady states has been referred to in the literature as the steady state fluctuation theorem or ssft in this paper we demonstrate experimentally the application of the ft to nonequilibrium steady states using a colloidal particle localized in a translating optical trap furthermore we show for this colloidal system that the ft holds under nonequilibrium steady states for all time and not just in the long time limit as in the ssft

asymptotic behavior of thermal nonequilibrium steady states for a driven chain of anharmonic oscillators we consider a model of heat conduction introduced in 6 which consists of a finite nonlinear chain coupled to two heat reservoirs at different temperatures we study the low temperature asymptotic behavior of the invariant measure we show that in this limit the invariant measure is characterized by a variational principle the main technical ingredients are some control theoretic arguments to extend the freidlin wentzell theory of large deviations to a class of degenerate diffusions

multiple symbol differential detection with interference suppression a multiple symbol differential detector is formulated for m ary differential phase shift keying modulation where the channel state information is unknown to the receiver the maximum likelihood decision statistic is derived for the detector and its performance is demonstrated by analysis and simulation under the gaussian assumption for the aggregate interference plus noise an exact expression for the symbol pairwise error probability is developed for m ary differential phase shift keying modulation over a diversity slow fading rayleigh channel in the presence of an interference source a simpler expression of the pairwise error probability is developed for the asymptotic case of large signal to noise ratio and small signal to interference ratio it is shown that with an increasing observation interval the performance of the differential detector over an unknown channel approaches that of optimum combining with known channel

error performance of multiple symbol differential detection of psk signals transmitted over correlated rayleigh fading channels the error performance of multiple symbol differential detection of uncoded qpsk signals transmitted over correlated rayleigh fading channels is studied the optimal detector is presented along with an exact expression for the corresponding pairwise error event probability it is shown that multiple symbol differential detection is a very effective strategy for eliminating the irreducible error floor associated with a conventional differential detector in all of the cases investigated a detector with an observation interval as small as two symbols is sufficient for this purpose it is also found that the error performance of a multiple symbol differential detector is not sensitive to the mismatch between the decoding metric and the channel fading statistics

chaotic principle an experimental test abstract the chaotic hypothesis discussed in gallavotti and cohen 1995 is tested experimentally in a simple conduction model besides a confirmation of the hypothesis predictions the results suggest the validity of the hypothesis in the much wider context in which as the forcing strength grows the attractor ceases to be an anosov system and becomes an axiom a attractor a first text of new predictions is also attempted

fluctuation theorems for quantum master equations a quantum fluctuation theorem for a driven quantum subsystem interacting with its environment is derived based solely on the assumption that its reduced density matrix obeys a closed evolution equation i e a quantum master equation qme quantum trajectories and their associated entropy heat and work appear naturally by transforming the qme to a time dependent liouville space basis that diagonalizes the instantaneous reduced density matrix of the subsystem a quantum integral fluctuation theorem a steady state fluctuation theorem and the jarzynski relation are derived in a similar way as for classical stochastic dynamics

inequalities for non equilibrium fluctuations of work five previously unknown inequalities relating equilibrium free energy differences and non equilibrium work fluctuations are derived and lucid path to derivation of many similar inequalities is presented these results are based upon combined exploitation of the jarzynski equality and the generalization of the scheme for producing uncertainty type inequalities due to h weyl the inequalities may possibly lead to better understanding of behavior of the equilibrium free energy estimators from non equilibrium experimental data in many important applications concerning biological chemical and physical molecular processes

steady states invariant measures and response theory using the method of computer simulation we test the predictions of nonlinear response theory for classical systems subject to dissipative external fields we provide convincing numerical evidence that kawasaki methods agree with both the transient time correlation function predictions and with a direct measurement of the nonlinear response furthermore this numerical agreement is observed over a time scale which is sufficiently long for the response to have relaxed to within ensuremath sim 1 of its nonequilibrium steady state value this is in spite of the fact that in the steady state the n particle distribution function ultimately becomes fractal we discuss the normalization of the kawasaki distribution and derive a lagrangian form of the kawasaki response function and show that it is consistent with predictions that are obtained using a natural invariant measure for nonequilibrium steady states c 1995 the american physical society

direct measurement of weakly nonequilibrium system entropy is consistent with gibbs shannon form stochastic thermodynamics extends classical thermodynamics to small systems in contact with one or more heat baths it can account for the effects of thermal fluctuations and describe systems far from thermodynamic equilibrium a basic assumption is that the expression for shannon entropy is the appropriate description for the entropy of a nonequilibrium system in such a setting here we measure experimentally this function in a system that is in local but not global equilibrium our system is a micron scale colloidal particle in water in a virtual double well potential created by a feedback trap we measure the work to erase a fraction of a bit of information and show that it is bounded by the shannon entropy for a two state system further by measuring directly the reversibility of slow protocols we can distinguish unambiguously between protocols that can and cannot reach the expected thermodynamic bounds

derivation of stokes law from kirkwood s formula and the green kubo formula via large deviation theory we study the friction coefficient of a macroscopic sphere in a viscous fluid at low reynolds number first kirkwood s formula for the friction coefficient is reviewed on the basis of the hamiltonian description of particle systems according to this formula the friction coefficient is expressed in terms of the stress correlation on the surface of the macroscopic sphere then with the aid of large deviation theory we relate the surface stress correlation to the stress correlation in the bulk of the fluid where the latter is characterized by the viscosity in the green kubo formula by combining kirkwood s formula and the green kubo formula in large deviation theory we derive stokes law without explicitly employing the hydrodynamic equations

theory of a systematic computational error in free energy differences systematic inaccuracy is inherent in any computational estimate of a nonlinear average due to the availability of only a finite number of data values n free energy differences delta f between two states or systems are critically important examples of such averages previous work has demonstrated empirically that the finite sampling error can be very large many times k b t in delta f estimates for simple molecular systems here we present a theoretical description of the inaccuracy including the exact solution of a sample problem the precise asymptotic behavior in terms of 1 n for large n the identification of a universal law and numerical illustrations the theory relies on corrections to the central and other limit theorems

multiple symbol differential detection with diversity reception in this letter we first consider the maximum likelihood sequence estimator for multiple symbol differential detection msdd over the slow fading diversity channel since this optimum decision metric results in a complex receiver implementation whose average bit error probability bep performance is difficult if not impossible to obtain analytically we then focus our attention on evaluating the average bep for msdd with diversity reception in the form of postdetection equal gain combining egc giving emphasis to its ability to bridge the gap between egc of conventional differentially detected m psk and maximal ratio combining of coherently detected m psk with differential encoding

work fluctuations in a time dependent harmonic potential rigorous results beyond the overdamped limit we investigate the stochastic motion of a brownian particle in the harmonic potential with a time dependent force constant it may describe the motion of a colloidal particle in an optical trap where the potential well is formed by a time dependent field we use the path integral formalism to solve the langevin equation and the associated fokker planck kramers equation rigorous relations are derived to generate the probability density function for the time dependent nonequilibrium work production beyond the overdamped limit we find that the work distribution exhibits an exponential tail with a power law prefactor accompanied by an interesting oscillatory feature multiple pseudo locking unlocking transitions due to the inertial effect some exactly solvable cases are discussed in the overdamped limit

noncoherent sequence detection new noncoherent sequence detection algorithms for combined demodulation and decoding of coded linear modulations transmitted over additive white gaussian noise channels possibly affected by intersymbol interference are presented optimal sequence detection in the presence of a random rotation of the signal phase assumed to be constant during the entire transmission requires a receiver complexity exponentially increasing with the duration of the transmission based on proper approximations simple suboptimal detection schemes based on the viterbi algorithm are presented whose performance approaches that of coherent detection in a companion paper by colavolpe and raheli see ibid vol 47 no 9 p 1303 7 1999 noncoherent sequence detection is extended to continuous phase modulations in the proposed schemes the tradeoff between complexity and performance is simply controlled by a parameter referred to as implicit phase memory and the number of states of a trellis diagram besides being realizable these schemes have the convenient feature of allowing us to remove the constant phase assumption and encompass time varying phase models the proposed schemes compare favorably with other solutions previously proposed in the technical literature

quantum work fluctuation theorem exact case study for a perturbed oscillator we analytically explore the fluctuation of the work induced entropy production of an externally perturbed quantum harmonic oscillator interacting with several reservoirs the quantum fluctuation of the work amounts to a non gaussian fluctuation of the entropy production which interpolates the gaussian and the poissonian distributions at high and low temperature regimes also it is shown that the corresponding fluctuation theorem symmetry is rigorously satisfied

unified treatment of the quantum fluctuation theorem and the jarzynski equality in terms of microscopic reversibility there are two related theorems which hold even in far from equilibrium namely fluctuation theorem and jarzynski equality fluctuation theorem states the existence of symmetry of fluctuation of entropy production while the jarzynski equality enables us to estimate the free energy change between two states by using irreversible processes on the other hand the relationship between these theorems was investigated by crooks phys rev e 60 2721 1999 for the classical stochastic systems in this paper we derive quantum analogues of fluctuation theorem and jarzynski equality in terms of microscopic reversibility in other words the quantum analog of the work by crooks is presented also for the quasiclassical langevin system microscopically reversible condition is confirmed

multiple bit differential detection of offset qpsk analogous to multiple symbol differential detection of quadrature phase shift keying qpsk a multiple bit differential detection scheme is described for offset qpsk that also exhibits continuous improvement in performance with increasing observation interval being derived from maximum likelihood considerations together with the representation of differentially encoded offset qpsk as a continuous phase modulation the proposed scheme is purported to be the most power efficient scheme for such a modulation and detection method

note on two theorems in nonequilibrium statistical mechanics an attempt is made to clarify the difference between a theorem derived by evans and searles in 1994 on the statistics of trajectories in phase space and a theorem proved by the authors in 1995 on the statistics of fluctuations on phase space trajectory segments in a nonequilibrium stationary state

smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics this paper reviews various applications of the theory of smooth dynamical systems to conceptual problems of nonequilibrium statistical mecanics we adopt a new point of view which has emerged progressively in recent years and which takes seriously into account the chaotic character of the microscopic time evolution the emphasis is on nonequilibrium steady states rather than the traditional approach to equilibrium point of view of boltzmann the nonequilibrium steady states in presence of a gaussian thermostat are described by srb measures in terms of these one can prove the gallavotti cohen fluctuation theorem one can also prove a general linear response formula and study its consequences which are not restricted to near equilibrium situations at equilibrium one recovers in particular the onsager reciprocity relations under suitable conditions the nonequilibrium steady states satisfy the pairing theorem of dettmann and morriss the results just mentioned hold so far only for classical systems they do not involve large size i e they hold without a thermodynamic limit

fluctuation theorem uncertainty relation the fluctuation theorem is the fundamental equality in nonequilibrium thermodynamics that is used to derive many important thermodynamic relations such as the second law of thermodynamics and the jarzynski equality recently the thermodynamic uncertainty relation was discovered which states that the fluctuation of observables is lower bounded by the entropy production in the present letter we derive a thermodynamic uncertainty relation from the fluctuation theorem we refer to the obtained relation as the fluctuation theorem uncertainty relation and it is valid for arbitrary dynamics stochastic as well as deterministic and for arbitrary antisymmetric observables for which a fluctuation theorem holds we apply the fluctuation theorem uncertainty relation to an overdamped langevin dynamics for an antisymmetric observable we demonstrate that the antisymmetric observable satisfies the fluctuation theorem uncertainty relation but does not satisfy the relation reported for current type observables in continuous time markov chains moreover we show that the fluctuation theorem uncertainty relation can handle systems controlled by time symmetric external protocols in which the lower bound is given by the work exerted on the systems

identification of damping part 3 symmetry preserving methods abstract in two recent papers adhikari and woodhouse 2001 journal of sound and vibration243 43 61 63 88 methods were proposed to identify viscous and non viscous damping models for vibrating systems using measured complex frequencies and mode shapes in many cases the identified damping matrix becomes asymmetric a non physical result methods are presented here to identify damping models which preserve symmetry of the system both viscous and non viscous models are considered the procedure is based on a constrained error minimization approach and uses only experimentally identified complex modes and complex natural frequencies together with for the non viscous model the mass matrix of the system the methods are illustrated by numerical examples

the performance of trellis coded mdpsk with multiple symbol detection the idea of using a multiple more than two symbol observation interval to improve error probability performance is applied to differential detection of trellis coded multiple phase shift keying mpsk over an additive white gaussian noise awgn channels an equivalent euclidean distance measure per trellis branch is determined for this detection scheme this is used to define an augmented larger multiplicity trellis code whose distance measure is the conventional squared euclidean distance typical of conventional trellis coded modulation on the awgn such an augmented multiple trellis code is a convenient mathematical tool for simplifying the analysis results are obtained by a combination of analysis and computer simulation it is shown that only a slight increase e g one symbol in the length of the observation interval will provide a significant improvement in bit error probability performance

impact of diversity reception on fading channels with coded modulation ii differential block detection for pt i see ibid vol 45 no 6 p 563 572 1997 we study coded modulation with block differential detection in an arbitrarily correlated rician fading channel with space diversity coded differential q psk is included in our analysis as a special case a metric is chosen that is optimum for perfect interleaving slow fading and independent diversity branches for slow fading we compare the the cutoff rates of the channels resulting from different choices of block length n and diversity index m specifically we show that block detection with diversity may or may not generate a better coding channel than usual differential detection according to the code selected and the combination of values of m and n in particular for low diversity orders m 1 2 and for low to medium code rates differential detection is still an optimal or near optimal solution while for high diversity orders m spl ges 2 and medium to high code rates up to uncoded modulation block detection with n 2 can provide a significant gain an error floor always exists when fading is fast it decreases exponentially with the product of code diversity and space diversity so that the latter emerges as a very effective technique for lowering the error floor of a system affected by fast fading performance examples based on actual coding schemes are also shown

the phase of a vector perturbed by gaussian noise and differentially coherent receivers some results are presented regarding the asymptotic distribution of the phase of a vector perturbed by gaussian noise it is shown that for large signal to noise ratio the asymptotic distribution of the phase is of the tikhonov type this framework is then used for the synthesis of differentially coherent receiver structures one for m ary phase shift keying mpsk and the other for minimum shift keying msk the first structure bridges the performance gap between coherent and differentially coherent demodulation of mpsk the msk receiver uses matched filtering with differential demodulation

microscopic analysis of clausius duhem processes given a thermodynamic process which carries a system from one equilibrium state to another we construct a quantity whose average over an ensemble of microscopic realizations of the process depends only on these end states even if at intermediate times the system is out of equilibrium this result 1 can be used to express the entropy difference between two equilibrium states in terms of an irreversible process connecting them 2 leads to two statistical statements of the clausius duhem inequality and 3 can be generalized to situations in which the system begins and or ends in nonequilibrium states

distribution of work in isothermal nonequilibrium processes diffusive motion in an externally driven potential is considered it is shown that the distribution of work required to drive the system from an initial equilibrium state to another is gaussian for slow but finite driving our result is obtained by projection method techniques exploiting a small parameter defined as the switching rate between the two states of the system the exact solution for a simple model system shows that such an expansion may fail in higher orders since the mean and the variance following from the exact distribution show nonanalytic behavior

generalized jarzynski s equality in inhomogeneous markov chains a rigorous mathematical theory of generalized jarzynski s equality in inhomogeneous markov chains is given then we explain its physical meaning and applications through several previous work including the original works of jarzynski phys rev lett 78 2690 1997 phys rev e 56 5018 1997 j stat phys 96 415 1999 j stat phys 98 77 2000 and crooks j stat phys 90 1481 1998 phys rev e 60 2721 1999 phys rev e 61 2361 2000 hatano sasa equality phys rev e 86 3463 2001 and the gibbs free energy differences in stoichiometric chemical systems by the way we also consider the denumerable case

reduced state sequence estimation with set partitioning and decision feedback a reduced state sequence estimator for linear intersymbol interference channels is described the estimator uses a conventional viterbi algorithm with decision feedback to search a reduced state subset trellis that is constructed using set partitioning principles the complexity of maximum likelihood sequence estimation mlse due to the length of the channel memory and the size of the signal set is systematically reduced an error probability analysis shows that a good performance complexity tradeoff can be obtained in particular the results indicate that the required complexity to achieve the performance of mlse is independent of the size of the signal set for large enough signal sets simulation results are provided for two partial response systems a simple technique for quadrature partial response signaling qprs is described that eliminates the quasicatastrophic nature of the ml trellis

estimating entropy production by machine learning of short time fluctuating currents thermodynamic uncertainty relations turs are the inequalities which give lower bounds on the entropy production rate using only the mean and the variance of fluctuating currents since the turs do not refer to the full details of the stochastic dynamics it would be promising to apply the turs for estimating the entropy production rate from a limited set of trajectory data corresponding to the dynamics here we investigate a theoretical framework for estimation of the entropy production rate using the turs along with machine learning techniques without prior knowledge of the parameters of the stochastic dynamics specifically we derive a tur for the short time region and prove that it can provide the exact value not only a lower bound of the entropy production rate for langevin dynamics if the observed current is optimally chosen this formulation naturally includes a generalization of the turs with the partial entropy production of subsystems under autonomous interaction which reveals the hierarchical structure of the estimation we then construct estimators on the basis of the short time tur and machine learning techniques such as the gradient ascent by performing numerical experiments we demonstrate that our learning protocol performs well even in nonlinear langevin dynamics we also discuss the case of markov jump processes where the exact estimation is shown to be impossible in general our result provides a platform that can be applied to a broad class of stochastic dynamics out of equilibrium including biological systems

prior predictive value from fast growth simulations error analysis and bias estimation variants of fluctuation theorems recently discovered in the statistical mechanics of nonequilibrium processes may be used for the efficient determination of high dimensional integrals as typically occurring in bayesian data analysis in particular for multimodal distributions monte carlo procedures not relying on perfect equilibration are advantageous we provide a comprehensive statistical error analysis for the determination of the prior predictive value the evidence in a bayes problem building on a variant of the jarzynski equation special care is devoted to the characterization of the bias intrinsic to the method and statistical errors arising from exponential averages we also discuss the determination of averages over multimodal posterior distributions with the help of a consequence of the crooks relation all our findings are verified by extensive numerical simulations of two model systems with bimodal likelihoods

jarzynski equality in van der pol and rayleigh oscillators we have studied the jarzynski equality je in van der pol and rayleigh oscillators which are typical deterministic non hamiltonian models but not expected to rigorously satisfy the je because they are not reversible our simulations that calculate the contribution to the work w of an applied ramp force with a duration show that the je approximately holds for a fairly wide range of including 0 and except for t where t denotes the period of relaxation oscillations in the limit cycle the work distribution function wdf is shown to be non gaussian with the u shaped structure for a strong damping parameter the dependence of r k b tln e w obtained by our simulations is semiquantitatively elucidated with the use of a simple expression for limit cycle oscillations where the bracket expresses an average over the wdf the result obtained in self excited oscillators is in contrast with the fact that the je holds in the nose hoover oscillator which also belongs to deterministic non hamiltonian models

quantification of non viscous damping in discrete linear systems abstract the damping forces in a multiple degree of freedom engineering dynamic system may not be accurately described by the familiar viscous damping model the purpose of this paper is to develop indices to quantify the extent of any departures from this model in other words the amount of non viscosity of damping in discrete linear systems four indices are proposed two of these indices are based on the non viscous damping matrix of the system a third index is based on the residue matrices of the system transfer functions and the fourth is based on the measured complex modes of the system the performance of the proposed indices is examined by considering numerical examples

convergence of large deviation estimators we study the convergence of statistical estimators used in the estimation of large deviation functions describing the fluctuations of equilibrium nonequilibrium and manmade stochastic systems we give conditions for the convergence of these estimators with sample size based on the boundedness or unboundedness of the quantity sampled and discuss how statistical errors should be defined in different parts of the convergence region our results shed light on previous reports of phase transitions in the statistics of free energy estimators and establish a general framework for reliably estimating large deviation functions from simulation and experimental data and identifying parameter regions where this estimation converges

reexamination of experimental tests of the fluctuation theorem the fluctuation theorem and the jarzynski equality are examined in the light of recent experimental tests for a particle dragged through a solvent it is shown that q the heat exchanged with the reservoir does not obey the jarzynski equality due to slowly decaying tails in its distribution for molecular stretching experiments substantial corrections to the jarzynski equality can result from not measuring the force at the end of the molecule that is moved we also present a proof of the fluctuation theorem for langevin dynamics that is considerably simpler than the standard proof

the mclennan zubarev steady state distribution and fluctuation theorems abstract the mclennan zubarev steady state distribution is studied in the connection with fluctuation theorems we derive the mclennan zubarev steady state distribution from the nonequilibrium detailed balance relation then considering the cumulant function or cumulant functional two fluctuation theorems for entropy and for currents are proved using the fluctuation theorem for currents the current is expanded in terms of thermodynamic forces in the lowest order of the thermodynamic force we find that the transport coefficient satisfies the onsager s reciprocal relation in the next order we derived the correction term to the green kubo formula

work distribution functions in polymer stretching experiments we compute the distribution of the work done in stretching a gaussian polymer made of n monomers at a finite rate for a one dimensional polymer undergoing rouse dynamics the work distribution is a gaussian and we explicitly compute the mean and width the two cases where the polymer is stretched either by constraining its end or by constraining the force on it are examined we discuss connections to jarzynski s equality and the fluctuation theorems

initial ensemble dependence of jarzynski equality in the thermodynamic limit we investigate the initial ensemble dependence of the jarzynski relation for nonequilibrium work performed on a classical system in the thermodynamic limit it is shown that the jarzynski equality holds also for a microcanonical ensemble only if the work process is quasi statically slow if work is performed by a rapid perturbation the average of exponentiated work expanded on a microcanonical system markedly deviates from the jarzynski equality such deviation in fact quantifies the ratio of the energy distributions of nonequilibrium states in relative to equilibrium distribution we exemplify these points in a simple model system both for the cases of deterministic and stochastic dynamics

on noncoherent receivers for dstm in spatially correlated fading in this letter we derive a multiple symbol differential detection msdd and a novel msdd based decision feedback differential detection ms dfdd receiver for differential space time modulation transmitted over spatially correlated multiple input multiple output fading channels we show that ms dfdd outperforms previously proposed dfdd schemes that are based on scalar and vector prediction sp dfdd and vp dfdd in addition we prove that at high signal to noise ratio snr vp dfdd is equivalent to sp dfdd and thus fails to properly exploit the spatial fading correlations

a local fluctuation theorem abstract a mechanism for the validity of a local version of the fluctuation theorem uniform in the system size is discussed for a reversible chain of weakly coupled anosov systems

multiple trellis coded modulation mtcm the authors demonstrate a trellis coded modulation technique referred to as multiple trellis coded modulation mtcm wherein more than one channel symbol per trellis branch is transmitted they have found simple two state trellis codes for symmetric mpsk multiple phase shift keying and am modulations that can achieve 3 db gain over uncoded modulation at very high signal to noise ratios without bandwidth expansion or reduction in information bit rate the gain of these codes with respect to previously reported two state trellis codes is between 1 and 2 db at very high signal to noise ratios depending on the number of bits per hertz transmitted these gains are achieved for those of the equivalent conventional trellis codes with the same number of states in the trellis diagram the authors note that additional computations per branch are needed for the multiple trellis coding scheme the concept can be extended to a higher number of states and other types of modulations

computing the optimal protocol for finite time processes in stochastic thermodynamics asking for the optimal protocol of an external control parameter that minimizes the mean work required to drive a nanoscale system from one equilibrium state to another in finite time schmiedl and seifert t schmiedl and u seifert phys rev lett 98 108301 2007 found the euler lagrange equation to be a nonlocal integrodifferential equation of correlation functions for two linear examples we show how this integrodifferential equation can be solved analytically for nonlinear physical systems we show how the optimal protocol can be found numerically and demonstrate that there may exist several distinct optimal protocols simultaneously and we present optimal protocols that have one two and three jumps respectively

thermodynamic uncertainty relations including measurement and feedback thermodynamic uncertainty relations quantify how the signal to noise ratio of a given observable is constrained by dissipation fluctuation relations generalize the second law of thermodynamics to stochastic processes we show that any fluctuation relation directly implies a thermodynamic uncertainty relation considerably increasing their range of applicability in particular we extend thermodynamic uncertainty relations to scenarios which include measurement and feedback since feedback generally breaks time reversal invariance the uncertainty relations involve quantities averaged over the forward and the backward experiment defined by the associated fluctuation relation this implies that the signal to noise ratio of a given experiment can in principle become arbitrarily large as long as the corresponding backward experiment compensates e g by being sufficiently noisy we illustrate our results with the szilard engine as well as work extraction by free energy reduction in a quantum dot

on the llr metrics for dpsk modulations over two symbol observation intervals for the flat rician fading channel we consider the differential phase shift keying modulation over the flat rician fading channel with perfect channel model information pcmi and derive the two symbol observation interval log likelihood ratio llr metric from first principles the work generalizes the previous llr derivations in 16 19 and demonstrates the necessity of the knowledge of the statistical channel model in the exact llr computation assuming the channel is slowly time varying we also propose a simple approximate llr metric based on the generalized likelihood ratio test glrt which requires only the information of the noise spectral density the advantage of the newly derived pcmi llr metric over the approximate metric and the other llr metrics in the literature is explained from the information theoretic perspective via the generalized mutual information computer simulations are also provided to demonstrate the superiority of the pcmi llr metric in both error rate performance and convergence speed for iterative decoding of turbo and low density parity check codes in practical systems this paper aims to present the fundamental principles of llr computation emphasizing the importance of selecting the appropriate metric for iterative decoding over fading channels

frequency offset invariant multiple symbol differential detection of mpsk multiple symbol differential detection msdd of differentially encoded phase shift keying psk signals in the presence of random frequency variation and additive white gaussian noise is studied it is shown that frequency variation distorts the transmitted signal through attenuating its amplitude and introducing a time varying phase shift to the information symbols a double differential psk ddpsk modulation scheme is then introduced and a msdd for detecting ddpsk signals in the presence of frequency offset is proposed it is shown that the proposed receiver is robust to the distortions caused by the random frequency variation a lower bound on the error probability of the proposed msdd receiver is also derived and compared to that of an autocorrelation demodulator for the case where the observation interval approaches infinity

an assessment of damping identification methods a study is carried out into the philosophy and performance of different approaches for the determination of linear viscous damping in elasto mechanical systems the methods studied include a closed form solution identification methods based on inverting the matrix of receptances energy expressions developed from single frequency excitation and responses as well as first order perturbation methods the work is concentrated particularly upon modal truncation and how this affects the distribution of matrix terms and the ability of the identified damping together with known mass and stiffness terms to reproduce the complex eigenvalues and eigenvectors of the full order system a simulated example is used to illustrate various points covered in the theoretical discussion of the methods considered

bias and error in estimates of equilibrium free energy differences from nonequilibrium measurements in 1997 jarzynski proved a remarkable equality that allows one to compute the equilibrium free energy difference deltaf between two states from the probability distribution of the nonequilibrium work w done on the system to switch between the states e deltaf kappat e w kappat jarzynski c 1997 phys rev lett 87 2690 2693 the jarzynski equality provides a powerful free energy difference estimator from a set of n irreversible experiments and is closely related to free energy perturbation a common computational technique for estimating free energy differences despite the many applications of the jarzynski estimator its behavior is only poorly understood in this article we derive the large n limit for the jarzynski estimator bias variance and mean square error that is correct for arbitrary perturbations we then analyze the properties of the jarzynski estimator for all n when the probability distribution of work values is gaussian as occurs for example in the near equilibrium regime this allows us to quantitatively compare it to two other free energy difference estimators the mean work estimator and the fluctuation dissipation theorem estimator we show that for near equilibrium switching the jarzynski estimator is always superior to the mean work estimator and is even superior to the fluctuation dissipation estimator for small n the jarzynski estimator bias is shown to be the dominant source of error in many cases our expression for the bias is used to develop a bias corrected jarzynski free energy difference estimator in the near equilibrium regime

multiple symbol differential detection of mpsk a differential detection technique for mpsk multiple phase shift keying which uses a multiple symbol observation interval is presented and its performance is analyzed and simulated the technique makes use of maximum likelihood sequence estimation of the transmitted phases rather than symbol by symbol detection as in the conventional differential detection thus the performance of this multiple symbol detection scheme fills the gap between conventional two symbol observation differentially coherent detection of mpsk and ideal coherent of mpsk with differential encoding the amount of improvement gained over conventional differential detection depends on the number of phases m and the number of additional symbol intervals added to the observation what is particularly interesting is that substantial performance improvement can be obtained for only one or two additional symbol intervals of observation the analysis and simulation results presented are for uncoded mpsk

identification of damping part 1 viscous damping abstract characterization of damping forces in a vibrating structure has long been an active area of research in structural dynamics the most common approach is to use viscous damping where the instantaneous generalized velocities are the only relevant state variables that affect damping forces however viscous damping is by no means the only damping model within the scope of linear analysis any model which makes the energy dissipation functional non negative is a possible candidate for a valid damping model this paper and its companion see pp 63 88 of this issue are devoted to developing methodologies for identification of such general damping models responsible for energy dissipation in a vibrating structure this paper considers identification of viscous damping under circumstances when the actual damping model in the structure is non viscous a method is presented to obtain a full non proportional viscous damping matrix from complex modes and complex natural frequencies it is assumed that the damping is small so that a first order perturbation method is applicable the proposed method and several related issues are discussed by considering numerical examples based on a linear array of damped spring mass oscillators it is shown that the method can predict the spatial location of damping with good accuracy and also give some indication of the correct mechanism of damping

nonequilibrium thermodynamics of feedback control we establish a general theory of feedback control on classical stochastic thermodynamic systems and generalize nonequilibrium equalities such as the fluctuation theorem and the jarzynski equality in the presence of feedback control with multiple measurements our results are generalizations of the previous relevant works to the situations with general measurements and multiple heat baths the obtained equalities involve additional terms that characterize the information obtained by measurements or the efficacy of feedback control a generalized szilard engine and a feedback controlled ratchet are shown to satisfy the derived equalities

a unified approach to the probability of error for noncoherent and differentially coherent modulations over generalized fading channels we present a unified approach to determine the exact bit error rate ber of noncoherent and differentially coherent modulations with single and multichannel reception over additive white gaussian noise and generalized fading channels the multichannel reception results assume independent fading in the channels and are applicable to systems that employ post detection equal gain combining our approach relies on an alternate form of the marcum q function and leads to expressions of the ber involving a single finite range integral which can be readily evaluated numerically aside from unifying the past results the new approach also allows for a more general solution to the problem in that it includes many situations that in the past defied a simple solution the best example of this occurs for multichannel reception where the fading on each channel need not be identically distributed nor even distributed according to the same family of distributions

fluctuation theorem for hidden entropy production elimination of seemingly unnecessary variables in markovian models may cause a difference in the value of irreversible entropy production between the original and reduced dynamics we show that such difference which we call the hidden entropy production obeys an integral fluctuation theorem if all variables are time reversal invariant or if the density function is symmetric with respect to the change of sign of the time reversal antisymmetric variables the theorem has wide applicability since the proposed condition is mostly satisfied in the case where the hidden fast variables are equilibrated the main consequence of this theorem is that the entropy production decreases by the coarse graining procedure by contrast in the case where a stochastic process is obtained by coarse graining a deterministic and reversible dynamics the entropy production may increase implying that the integral fluctuation theorem should not hold for such reductions we reveal with an explicit example that the nonequilibrated time reversal antisymmetric variables play a crucial role in distinguishing these two cases thus guaranteeing the consistency of the presented theorem

fluctuation theorem for stochastic systems the fluctuation theorem describes the probability ratio of observing trajectories that satisfy or violate the second law of thermodynamics it has been proved in a number of different ways for thermostatted deterministic nonequilibrium systems in the present paper we show that the fluctuation theorem is also valid for a class of stochastic nonequilibrium systems the theorem is therefore not reliant on the reversibility or the determinism of the underlying dynamics numerical tests verify the theoretical result

fluctuation theorem with information exchange role of correlations in stochastic thermodynamics we establish the fluctuation theorem in the presence of information exchange between a nonequilibrium system and other degrees of freedom such as an observer and a feedback controller where the amount of information exchange is added to the entropy production the resulting generalized second law sets the fundamental limit of energy dissipation and energy cost during the information exchange our results apply not only to feedback controlled processes but also to a much broader class of information exchanges and provide a unified framework of nonequilibrium thermodynamics of measurement and feedback control

a unified performance analysis framework for differential detection in mimo rayleigh fading channels in this paper a unified framework for the analysis of differential detection dd schemes in time variant multiple input multiple output rayleigh fading channels is provided the present results are very general in that they apply to transmission with differential phase shift keying unitary differential space time modulation dstm and block dstm and reception with conventional dd cdd multiple symbol dd msdd decision feedback dd dfdd and differentially coherent detection cd new result for general quadratic forms of gaussian random variables are derived which allows us to obtain elegant closed form expressions for the pairwise error probabilities peps of the dominant error events of the considered detectors furthermore it is shown that a unified treatment of all considered detectors is possible with a properly defined effective signal to noise ratio esnr and a useful connection between msdd and minimum mean squared error mmse interpolation is established interesting novel results obtained from this analysis include i dstm constellations designed for cdd and cd are also optimum for msdd and dfdd ii the error floor entailed by msdd and dfdd in time variant fading decreases exponentially with the observation window size n and iii in time variant fading with effective normalized fading bandwidth bh efft msdd with n rarr infin suffers only from an snr loss of 1 2bh efft compared to cd whereas dfdd suffers from a diversity loss of 1 2bh efft

fluctuation theorem in rachet system the fluctuation theorem ft has been studied as a far from equilibrium theorem which relates the symmetry of entropy production to investigate the application of this theorem especially to biological physics we consider the ft for a tilted rachet system under natural assumptions the ft for steady state is derived

generalized jarzynski equality under nonequilibrium feedback control the jarzynski equality is generalized to situations in which nonequilibrium systems are subject to a feedback control the new terms that arise as a consequence of the feedback describe the mutual information content obtained by measurement and the efficacy of the feedback control our results lead to a generalized fluctuation dissipation theorem that reflects the readout information and they can be experimentally tested using small thermodynamic systems we illustrate our general results by introducing an information ratchet which can transport a brownian particle in one direction and extract positive work from the particle

hamiltonian derivation of a detailed fluctuation theorem we analyze the microscopic evolution of a system undergoing a far from equilibrium thermodynamic process explicitly accounting for the degrees of freedom of participating heat reservoirs we derive a hybrid result similar in form to both the fluctuation theorem and a statement of detailed balance we relate this result to the steady state fluctuation theorem and to a free energy relation valid far from equilibrium

phase transition in the jarzynski estimator of free energy differences the transition between a regime in which thermodynamic relations apply only to ensembles of small systems coupled to a large environment and a regime in which they can be used to characterize individual macroscopic systems is analyzed in terms of the change in behavior of the jarzynski estimator of equilibrium free energy differences from nonequilibrium work measurements given a fixed number of measurements the jarzynski estimator is unbiased for sufficiently small systems in these systems the directionality of time is poorly defined and the configurations that dominate the empirical average but which are in fact typical of the reverse process are sufficiently well sampled as the system size increases the arrow of time becomes better defined the dominant atypical fluctuations become rare and eventually cannot be sampled with the limited resources that are available asymptotically only typical work values are measured the jarzynski estimator becomes maximally biased and approaches the exponential of minus the average work which is the result that is expected from standard macroscopic thermodynamics in the proper scaling limit this regime change has been recently described in terms of a phase transition in variants of the random energy model in this paper this correspondence is further demonstrated in two examples of physical interest the sudden compression of an ideal gas and adiabatic quasistatic volume changes in a dilute real gas

rare events and the convergence of exponentially averaged work values equilibrium free energy differences are given by exponential averages of nonequilibrium work values such averages however often converge poorly as they are dominated by rare realizations i show that there is a simple and intuitively appealing description of these rare but dominant realizations this description is expressed as a duality between forward and reverse processes and provides both heuristic insights and quantitative estimates regarding the number of realizations needed for convergence of the exponential average analogous results apply to the equilibrium perturbation method of estimating free energy differences the pedagogical example of a piston and gas r c lua and a y grosberg j phys chem b 109 6805 2005 is used to illustrate the general discussion

the transient fluctuation theorem of sample entropy production for general stochastic processes the transient fluctuation theorem for stochastic processes was first put forward by d j searles and d j evans 1999 in the present paper it is rigorously proved that the transient fluctuation theorem tft of sample entropy production which is previously defined by jiang et al 2003 and reid et al 2005 and also called the general action functional up to boundary terms by lebowitz and spohn 1999 holds for general stochastic processes without the assumption of markovian homogeneous or stationary properties then the condition of our theorem is verified for various stochastic processes including homogeneous inhomogeneous markov chains and general diffusion processes among these cases the transient fluctuation theorems for inhomogeneous markov chains and general diffusion processes are rigorously derived for the first time

fundamental relation between entropy production and heat current we investigate the fundamental relation between entropy production rate and the speed of energy exchange between a system and baths in classical markov processes we establish the fact that quick energy exchange inevitably induces large entropy production in a quantitative form more specifically we prove two inequalities on instantaneous quantities one is applicable to general markov processes induced by heat baths and the other is applicable only to systems with the local detailed balance condition but is stronger than the former one we demonstrate the physical meaning of our result by applying to some specific setups in particular we show that our inequality is tight in the linear response regime

nd convolutional codes ii structural analysis for pt i see ibid vol 43 no 2 p 558 75 1997 the structural properties of a noncoherent coded system which incorporates convolutional codes in conjunction with multiple symbol noncoherent detection is presented in this second part of a two part paper where the performance analysis was provided in part i these convolutional codes are referred to as nd convolutional codes and they provide a general framework for various noncoherent coding systems including differential systems for several practical models of the carrier phase the exponential rate in which the error probability decays to zero derived in part i of the paper is used here to obtain the free equivalent distance of nd codes which is the single parameter dominating the error performance at large signal to noise ratios the free equivalent distance is upper bounded by the free nd distance which constitutes a more convenient and practical parameter to work with and it is the basis for a computer search for optimal nd codes the resultant codes of the computer search are compared to codes which are optimal for coherent detection and it is verified that the latter codes are not necessarily optimal for noncoherent detection since they exhibit in many cases a relatively small nd distance the ambiguity problem inherent to noncoherent systems is also treated in this paper in the general framework of nd catastrophic codes and necessary and sufficient conditions for catastrophic error propagation are identified

nonequilibrium fluctuations for linear diffusion dynamics we present the theoretical study on nonequilibrium neq fluctuations for diffusion dynamics in high dimensions driven by a linear drift force we consider a general situation in which neq is caused by two conditions i drift force not derivable from a potential function and ii diffusion matrix not proportional to the unit matrix implying nonidentical and correlated multidimensional noise the former is a well known neq source and the latter can be realized in the presence of multiple heat reservoirs or multiple noise sources we develop a statistical mechanical theory based on generalized thermodynamic quantities such as energy work and heat the neq fluctuation theorems are reproduced successfully we also find the time dependent probability distribution function exactly as well as the neq work production distribution p mathcal w in terms of solutions of nonlinear differential equations in addition we compute low order cumulants of the neq work production explicitly in two dimensions we carry out numerical simulations to check out our analytic results and also to get p mathcal w we find an interesting dynamic phase transition in the exponential tail shape of p mathcal w associated with a singularity found in solutions of the nonlinear differential equation finally we discuss possible realizations in experiments

stochastic thermodynamics with odd controlling parameters stochastic thermodynamics extends the notions and relations of classical thermodynamics to small systems that experience strong fluctuations the definitions of work and heat and the microscopically reversible condition are two key concepts in the current framework of stochastic thermodynamics herein we apply stochastic thermodynamics to small systems with odd controlling parameters and find that the definition of heat and the microscopically reversible condition are incompatible such a contradiction also leads to a revision to the fluctuation theorems and nonequilibrium work relations by introducing adjoint dynamics we find that the total entropy production can be separated into three parts with two of them satisfying the integral fluctuation theorem revising the definitions of work and heat and the microscopically reversible condition allows us to derive two sets of modified nonequilibrium work relations including the jarzynski equality the detailed crooks work relation and the integral crooks work relation we consider the strategy of shortcuts to isothermality as an example and give a more sophisticated explanation for the jarzynski like equality derived from shortcuts to isothermality

maximum likelihood differential detection of uncoded and trellis coded amplitude phase modulation over awgn and fading channels spl minus metrics and performance this paper derives metrics for maximum likelihood differential detection of uncoded and trellis coded mpsk and qam transmitted over rayleigh and rician fading channels receiver structures based on these metrics are proposed and their error probability performance analyzed and or simulated the results represent a generalization of the notion of multiple symbol differential detection previously introduced by the authors for mpsk over an awgn to the fading channel and other modulations for the coded cases ideal interleaving deinterleaving is assumed and furthermore the presence or absence of channel state information an interesting side result is that for a constant envelope modulation transmitted over a fading channel with unknown but rapidly varying phase error the other extreme to the slowly varying phase error case normally assumed for differential detection under certain practical assumptions it is shown that the optimum receiver is of the limiter discriminator type

identification of damping part 4 error analysis in previous papers s adhikari and j woodhouse 2001 journal of sound and vibration243 43 61 63 88 s adhikari and j woodhouse 2002 journal of sound and vibration251 477 490 methods were proposed to obtain the coefficient matrix for a viscous damping model or a non viscous damping model with an exponential relaxation function from measured complex natural frequencies and modes in all these works it has been assumed that exact complex natural frequencies and complex modes are known in reality this will not be the case the purpose of this paper is to analyze the sensitivity of the identified damping matrices to measurement errors by using numerical and analytical studies it is shown that the proposed methods can indeed be expected to give useful results from moderately noisy data provided a correct damping model is selected for fitting indications are also given of what level of noise in the measured modal properties is needed to mask the true physical behaviour