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

microcanonical quantum fluctuation theorems previously derived expressions for the characteristic function of work performed on a quantum system by a classical external force are generalized to arbitrary initial states of the considered system and to hamiltonians with degenerate spectra in the particular case of microcanonical initial states explicit expressions for the characteristic function and the corresponding probability density of work are formulated their classical limit as well as their relations to the corresponding canonical expressions are discussed a fluctuation theorem is derived that expresses the ratio of probabilities of work for a process and its time reversal to the ratio of densities of states of the microcanonical equilibrium systems with corresponding initial and final hamiltonians from this crooks type fluctuation theorem a relation between entropies of different systems can be derived which does not involve the time reversed process this entropy from work theorem provides an experimentally accessible way to measure entropies

the kawasaki distribution function for nonautonomous systems we describe a time dependent generalization of the kawasaki form of nonlinear response theory and verify the validity of our expressions against direct molecular dynamics computer simulations

quantum fluctuation relations for the lindblad master equation an open quantum system interacting with its environment can be modeled under suitable assumptions as a markov process described by a lindblad master equation in this work we derive a general set of fluctuation relations for systems governed by a lindblad equation these identities provide quantum versions of jarzynski hatano sasa and crooks relations in the linear response regime these fluctuation relations yield a fluctuation dissipation theorem fdt valid for a stationary state arbitrarily far from equilibrium for a closed system this fdt reduces to the celebrated callen welton kubo formula

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

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

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

symmetric informationally complete positive operator valued measures a new computer study we report on a new computer study of the existence of d2 equiangular lines in d complex dimensions such maximal complex projective codes are conjectured to exist in all finite dimensions and are the underlying mathematical objects defining symmetric informationally complete measurements in quantum theory we provide numerical solutions in all dimensions d 67 and moreover a putatively complete list of weyl heisenberg covariant solutions for d 50 a symmetry analysis of this list leads to new algebraic solutions in dimensions d 24 35 and 48 which are given together with algebraic solutions for d 4 15 and 19

quantum work statistics and resource theories bridging the gap through renyi divergences the work performed on or extracted from a nonautonomous quantum system described by means of a two point projective measurement approach is a stochastic variable we show that the cumulant generating function of work can be recast in the form of quantum r enyi ensuremath alpha divergences and by exploiting the convexity of this cumulant generating function derive a single parameter family of bounds for the first moment of work higher order moments of work can also be obtained from this result in this way we establish a link between quantum work statistics in stochastic approaches and resource theories for quantum thermodynamics a theory in which r enyi ensuremath alpha divergences take a central role to explore this connection further we consider an extended framework involving a control switch and an auxiliary battery which is instrumental to reconstructing the work statistics of the system we compare and discuss our bounds on the work distribution to findings on deterministic work studied in resource theoretic settings

complex hadamard matrices and equiangular tight frames abstract in this paper we give a new construction of parametric families of complex hadamard matrices of square orders and connect them to equiangular tight frames the results presented here generalize some of the recent ideas of bodmann et al 3 and extend the list of known equiangular tight frames in particular a 36 21 frame coming from a nontrivial cube root signature matrix is obtained for the first time

the cardinality balanced multi target multi bernoulli filter and its implementations it is shown analytically that the multitarget multibernoulli member recursion proposed by mahler has a significant bias in the number of targets to reduce the cardinality bias a novel multibernoulli approximation to the multi target bayes recursion is derived under the same assumptions as the member recursion the proposed recursion is unbiased in addition a sequential monte carlo smc implementation for generic models and a gaussian mixture gm implementation for linear gaussian models are proposed the latter is also extended to accommodate mildly nonlinear models by linearization and the unscented transform

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

stiffness of probability distributions of work and jarzynski relation for non gibbsian initial states we consider closed quantum systems into which baths may be integrated that are driven i e subject to time dependent hamiltonians our point of departure is the assumption that if systems start in non gibbsian states at some initial energies the resulting probability distributions of work may be largely independent of the specific initial energies it is demonstrated that this assumption has some far reaching consequences e g it implies the validity of the jarzynski relation for a large class of non gibbsian initial states by performing numerical analysis on integrable and nonintegrable spin systems we find the above assumption fulfilled for all examples considered through an analysis based on fermi s golden rule we partially relate these findings to the applicability of the eigenstate thermalization ansatz to the respective driving operators

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

causality response theory and the second law of thermodynamics we show that there is a close connection between the assumption of causality and the second law of thermodynamics we also show that for a class of classical reversible deterministic systems it is overwhelmingly improbable either to find causal steady states that violate the second law or anticausal states that satisfy the second law these arguments indicate that the existence of and the sign associated with the second law of thermodynamics is ultimately determined by causality our discussion employs a green kubo relation that we derive for an anticausal linear transport coefficient

thermodynamic cost of acquiring information connections between information theory and thermodynamics have proven to be very useful to establish bounding limits for physical processes ideas such as landauer s erasure principle and information assisted work extraction have greatly contributed not only to broadening our understanding about the fundamental limits imposed by nature but also paving the way for practical implementations of information processing devices the intricate information thermodynamics relation also entails a fundamental limit on parameter estimation establishing a thermodynamic cost for information acquisition we show that the amount of information that can be encoded in a physical system by means of a unitary process is limited by the dissipated work during the implementation of the process this includes a thermodynamic tradeoff for information acquisition likewise the information acquisition process is ultimately limited by the second law of thermodynamics this tradeoff for information acquisition may find applications in several areas of knowledge

test of fluctuation theorems in non markovian open quantum systems we study fluctuation theorems for open quantum systems with a non markovian heat bath using the approach of quantum master equations and examine the physical quantities that appear in those fluctuation theorems the approach of markovian quantum master equations to the fluctuation theorems was developed by esposito and mukamel phys rev e 73 046129 2006 we show that their discussion can be formally generalized to the case of a non markovian heat bath when the local system is linearly connected to a gaussian heat bath with the spectrum distribution of the drude form we found by numerically simulating the spin boson model in non markovian regime that the detailed balance condition is well satisfied except in a strongly nonequilibrium transient situation and hence our generalization of the definition of the entropy production is almost always legitimate therefore our generalization of the fluctuation theorem seems meaningful in wide regions

fluctuation theorems work is not an observable the characteristic function of the work performed by an external time dependent force on a hamiltonian quantum system is identified with the time ordered correlation function of the exponentiated system s hamiltonian a similar expression is obtained for the averaged exponential work which is related to the free energy difference of equilibrium systems by the jarzynski work theorem

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

the tasaki crooks quantum fluctuation theorem starting out from the recently established quantum correlation function expression of the characteristic function for the work performed by a force protocol on the system in talkner et al 2007 phys rev e 75 050102 preprint cond mat 0703213 the quantum version of the crooks fluctuation theorem is shown to emerge almost immediately by the mere application of an inverse fourier transformation

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

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

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

equiangular tight frames and unistochastic matrices we demonstrate that a complex equiangular tight frame composed of n vectors in dimension d denoted etf d n exists if and only if a certain bistochastic matrix univocally determined by n and d belongs to a special class of unistochastic matrices this connection allows us to find new complex etfs in infinitely many dimensions and to derive a method to introduce non trivial free parameters in etfs we present an explicit six parametric family of complex etf 6 16 which defines a family of symmetric povms minimal and maximal possible average entanglement of the vectors within this qubit qutrit family are described furthermore we propose an efficient numerical procedure to compute the unitary matrix underlying a unistochastic matrix which we apply to find all existing classes of complex etfs containing up to 20 vectors

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

occurrence of discontinuities in the performance of finite time quantum otto cycles we study a quantum otto cycle in which the strokes are performed in finite time the cycle involves energy measurements at the end of each stroke to allow for the respective determination of work we then optimize for the work and efficiency of the cycle by varying the time spent in the different strokes and find that the optimal value of the ratio of time spent on each stroke goes through sudden changes as the parameters of this cycle vary continuously the position of these discontinuities depends on the optimized quantity under consideration such as the net work output or the efficiency

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

optimal frames for erasures we study frames from the viewpoint of coding theory we introduce a numerical measure of how well a frame reconstructs vectors when some of the frame coefficients of a vector are lost and then attempt to find and classify the frames that are optimal in this setting

analytic implementations of the cardinalized probability hypothesis density filter the probability hypothesis density phd recursion propagates the posterior intensity of the random finite set rfs of targets in time the cardinalized phd cphd recursion is a generalization of the phd recursion which jointly propagates the posterior intensity and the posterior cardinality distribution in general the cphd recursion is computationally intractable this paper proposes a closed form solution to the cphd recursion under linear gaussian assumptions on the target dynamics and birth process based on this solution an effective multitarget tracking algorithm is developed extensions of the proposed closed form recursion to accommodate nonlinear models are also given using linearization and unscented transform techniques the proposed cphd implementations not only sidestep the need to perform data association found in traditional methods but also dramatically improve the accuracy of individual state estimates as well as the variance of the estimated number of targets when compared to the standard phd filter our implementations only have a cubic complexity but simulations suggest favorable performance compared to the standard joint probabilistic data association jpda filter which has a nonpolynomial complexity

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

heat transfer operators associated with quantum operations any quantum operation applied on a physical system is performed as a unitary transformation on a larger extended system if the extension used is a heat bath in thermal equilibrium the concomitant change in the state of the bath necessarily implies a heat exchange with it the dependence of the average heat transferred to the bath on the initial state of the system can then be found from the expectation value of a hermitian operator which is named as the heat transfer operator hto the purpose of this paper is to investigate the relation between the htos and the associated quantum operations since any given quantum operation on a system can be realized by different baths and unitaries many different htos are possible for each quantum operation on the other hand there are also strong restrictions on the htos which arise from the unitarity of the transformations the most important of these is the landauer erasure principle this paper is concerned with the question of finding a complete set of restrictions on the htos that are associated with a given quantum operation an answer to this question has been found only for a subset of quantum operations for erasure operations these characterizations are equivalent to the generalized landauer erasure principle for the case of generic quantum operations however it appears that the htos obey further restrictions which cannot be obtained from the entropic restrictions of the generalized landauer erasure principle

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

nonlinear fluctuation dissipation relations and stochastic models in nonequilibrium thermodynamics ii kinetic potential and variational principles for nonlinear irreversible processes abstract on the basis of a complete system of fluctuation dissipation relations considered in the first part of this series a variational principle for nonlinear irreversible processes is derived according to this principle the virtual entropy production functional analogous to the action in mechanics has an absolute minimum meaning on the real trajectory of a system the universal structure of the kinetic potential and the lagrangian of a system each contain complete information about fluctuations of macrovariables the connection of the lagrangian with the markovian kinetic operator of macrovariables is stated fundamental properties of dissipative potentials reflecting microscopic reversibility are considered the derived variational principle can be applied to closed systems the steady state of which is equilibrium as well as to open ones when external dynamic forces cause entropy flux through the system and put it into a steady non equilibrium state canonical transformations of macrovariables are considered

a unified approach for multi object triangulation tracking and camera calibration object triangulation 3 d object tracking feature correspondence and camera calibration are key problems for estimation from camera networks this paper addresses these problems within a unified bayesian framework for joint multi object tracking and camera calibration based on the finite set statistics methodology in contrast to the mainstream approaches an alternative parametrization is investigated for triangulation called disparity space the approach for feature correspondence is based on the probability hypothesis density phd filter and hence inherits the ability to handle the initialization of new tracks as well as the discrimination between targets and clutter within a bayesian paradigm the phd filtering approach then forms the basis of a camera calibration method from static or moving objects results are shown on simulated and real data

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

bayesian multi object filtering for pairwise markov chains random finite sets rfs are recent tools for addressing the multi object filtering problem the probability hypothesis density phd filter is an approximation of the multi object bayesian filter which results from the rfs formulation of the problem and has been used in many applications in the rfs framework it is assumed that each target and associated observation follow a hidden markov chain hmc model hmcs conveniently describe some physical properties of practical interest for practitioners but they also implicitly imply restrictive independence properties which in practice may not be satisfied by data in this paper we show that these structural limitations of hmc models can somehow be relaxed by embedding them into the more general class of pairwise markov chain pmc models we thus focus on the computation of the phd filter in a pmc framework and we propose a practical implementation of the phd filter for a particular class of pmc models

finite bath fluctuation theorem we demonstrate that a finite bath fluctuation theorem of the crooks type holds for systems that have been thermalized via weakly coupling them to a bath with energy independent finite specific heat we show that this theorem reduces to the known canonical and microcanonical fluctuation theorems in the two respective limiting cases of infinite and vanishing specific heat of the bath the result is elucidated by applying it to a two dimensional hard disk colliding elastically with few other hard disks in a rectangular box with perfectly reflecting walls

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

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

calculating work in adiabatic two level quantum markovian master equations a characteristic function method we present a characteristic function method to calculate the probability density functions of the inclusive work in adiabatic two level quantum markovian master equations these systems are steered by some slowly varying parameters and the dissipations may depend on time our theory is based on the interpretation of the quantum jump for the master equations in addition to the calculation we also find that the fluctuation properties of the work can be described by the symmetry of the characteristic functions which is exactly the same as in the case of isolated systems a periodically driven two level model is used to demonstrate the method

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

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

equiangular tight frames from paley tournaments abstract we prove the existence of equiangular tight frames having n 2 d 1 elements drawn from either c d or c d 1 whenever n is either 2 k 1 for k n or a power of a prime such that n 3 mod 4 we also find a simple explicit expression for the prime power case by establishing a connection to a 2 d element equiangular tight frame based on quadratic residues

a mathematical theorem as the basis for the second law thomson s formulation applied to equilibrium abstract there are several formulations of the second law and they may in principle have different domains of validity here a simple mathematical theorem is proven which serves as the most general basis for the second law namely the thomson formulation cyclic changes cost energy applied to equilibrium this formulation of the second law is a property akin to particle conservation normalization of the wave function it has been strictly proven for a canonical ensemble and made plausible for a micro canonical ensemble as the derivation does not assume time inversion invariance it is applicable to situations where persistent currents occur this clear cut derivation allows to revive the no perpetuum mobile in equilibrium formulation of the second law and to criticize some assumptions which are widespread in literature the result puts recent results devoted to foundations and limitations of the second law in proper perspective and structurizes this relatively new field of research

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

equiangular tight frames from complex seidel matrices containing cube roots of unity we derive easily verifiable conditions which characterize when complex seidel matrices containing cube roots of unity have exactly two eigenvalues the existence of such matrices is equivalent to the existence of equiangular tight frames for which the inner product between any two frame vectors is always a common multiple of the cube roots of unity we also exhibit a relationship between these equiangular tight frames complex seidel matrices and highly regular directed graphs we construct examples of such frames with arbitrarily many vectors

integral quantum fluctuation theorems under measurement and feedback control we derive integral quantum fluctuation theorems and quantum jarzynski equalities for a feedback controlled system and a memory which registers outcomes of the measurement the obtained equalities involve the information content which reflects the information exchange between the system and the memory and take into account the back action of a general measurement contrary to the classical case the generalized second law of thermodynamics under measurement and feedback control is reproduced from these equalities

fluctuation dissipation theorem for the microcanonical ensemble a derivation of the fluctuation dissipation theorem for the microcanonical ensemble is presented using linear response theory the theorem is stated as a relation between the frequency spectra of the symmetric correlation and response functions when the system is not in the thermodynamic limit this result can be viewed as an extension of the fluctuation dissipation relations to a situation where dynamical fluctuations determine the response therefore the relation presented here between equilibrium fluctuations and response can have a very different physical nature from the usual one in the canonical ensemble these considerations imply that the fluctuation dissipation theorem is not restricted to the context of the canonical ensemble where it is usually derived dispersion relations and sum rules are also obtained and discussed in the present case although analogous to the kramers kronig relations they are not related to the frequency spectrum but to the energy dependence of the response function

equivalence of two bochkov kuzovlev equalities in quantum two level systems we present two kinds of bochkov kuzovlev work equalities in a two level system that is described by a quantum markovian master equation one is based on multiple time correlation functions and the other is based on the quantum trajectory viewpoint we show that these two equalities are indeed equivalent importantly this equivalence provides us a way to calculate the probability density function of the quantum work by solving the evolution equation for its characteristic function we use a numerical model to verify these results

convergence results for the particle phd filter bayesian single target tracking techniques can be extended to a multiple target environment by viewing the multiple target state as a random finite set but evaluating the multiple target posterior distribution is currently computationally intractable for real time applications a practical alternative to the optimal bayes multitarget filter is the probability hypothesis density phd filter which propagates the first order moment of the multitarget posterior instead of the posterior distribution itself it has been shown that the phd is the best fit approximation of the multitarget posterior in an information theoretic sense the method avoids the need for explicit data association as the target states are viewed as a single global target state and the identities of the targets are not part of the tracking framework sequential monte carlo approximations of the phd using particle filter techniques have been implemented showing the potential of this technique for real time tracking applications this paper presents mathematical proofs of convergence for the particle filtering algorithm and gives bounds for the mean square error

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

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

nonequilibrium green s function s approach to the calculation of work statistics the calculation of work distributions in a quantum many body system is of significant importance and also of formidable difficulty in the field of nonequilibrium quantum statistical mechanics to solve this problem inspired by the schwinger keldysh formalism we propose the contour integral formulation for work statistics based on this contour integral we show how to do the perturbation expansion of the characteristic function of work cfw and obtain the approximate expression of the cfw to the second order of the work parameter for an arbitrary system under a perturbative protocol we also demonstrate the validity of fluctuation theorems by utilizing the kubo martin schwinger condition finally we use noninteracting identical particles in a forced harmonic potential as an example to demonstrate the powerfulness of our approach

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

labeled random finite sets and multi object conjugate priors the objective of multi object estimation is to simultaneously estimate the number of objects and their states from a set of observations in the presence of data association uncertainty detection uncertainty false observations and noise this estimation problem can be formulated in a bayesian framework by modeling the hidden set of states and set of observations as random finite sets rfss that covers thinning markov shifts and superposition a prior for the hidden rfs together with the likelihood of the realization of the observed rfs gives the posterior distribution via the application of bayes rule we propose a new class of rfs distributions that is conjugate with respect to the multiobject observation likelihood and closed under the chapman kolmogorov equation this result is tested on a bayesian multi target tracking algorithm

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

a sharpening of the welch bounds and the existence of real and complex spherical t designs the welch bounds for a finite set of unit vectors are a family of inequalities indexed by t 1 2 ldots which describe how evenly spread the vectors are they have important applications in signal analysis where sequences giving equality in the first welch bound are known as welch bound equality sequences or as unit norm tight frames here we consider sequences of vectors giving equality in the higher order welch bounds these are seen to correspond to tight frames for the complex symmetric t tensors which we prove always exist we show that for t 1 the welch bounds can be sharpened for real vectors and again vectors giving equality always exist we give a unified treatment of various conditions for equality in both the real and complex cases in particular we give an explicit description of the corresponding cubature rules t designs our results set up a framework for the construction and classification several configurations of vectors of recent interest these include mutually unbiased bases complex equiangular lines spherical half designs projective t designs and minimisers of the higher order frame potential one interesting consequence is a construction of sets of complex equiangular lines which were previously unknown

convergence analysis of the gaussian mixture phd filter the gaussian mixture probability hypothesis density phd filter was proposed recently for jointly estimating the time varying number of targets and their states from a sequence of sets of observations without the need for measurement to track data association it was shown that under linear gaussian assumptions the posterior intensity at any point in time is a gaussian mixture this paper proves uniform convergence of the errors in the algorithm and provides error bounds for the pruning and merging stages in addition uniform convergence results for the extended kalman phd filter are given and the unscented kalman phd filter implementation is discussed

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

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

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

equiangular tight frames and fourth root seidel matrices in this paper we construct complex equiangular tight frames etfs in particular we study the grammian associated with an etf whose off diagonal entries consist entirely of fourth roots of unity these etfs are classified and we also provide some computational techniques which give rise to previously undiscovered etfs

characteristic functions based on a quantum jump trajectory characteristic functions cfs provide a very efficient method for evaluating the probability density functions of stochastic thermodynamic quantities and investigating their statistical features in quantum master equations qmes a conventional procedure for obtaining these functions is to resort to a first principles approach namely the evolution equations of the cfs of the combined system and its environment are obtained and then projected into the degrees of freedom of the system however the qmes can be unraveled by a quantum jump trajectory thermodynamic quantities such as the heat work and entropy production can be well defined along a trajectory hence on the basis of the notion of a trajectory can we straightforwardly derive these cfs e g their evolution equations this is essential to establish the self contained stochastic thermodynamics of a qme in this paper we show that it is indeed plausible and also simple particularly these equations are fully consistent with those obtained by the first principles method our results have practical significance they indicate that the quantum fluctuation relations could be verified by more realistic photocounting experiments

time dependent response theory and nonequilibrium free energy relations the mathematics of time dependent nonlinear response theory frequently leads to results which although formally exact are not amenable to experimental application or even to use in computer simulations here we give a rigorous derivation of a tractable expression for the thermostatted nonlinear response of classical many body systems to time dependent dissipative fields the theory also allows for the concurrent parametric transformation of the system hamiltonian our analysis shows once again the intimate relationship between nonequilibrium free energy relations such as the jarzynski equality and nonlinear response theory we make a few remarks concerning the maximum entropy production approximation

the gaussian mixture probability hypothesis density filter a new recursive algorithm is proposed for jointly estimating the time varying number of targets and their states from a sequence of observation sets in the presence of data association uncertainty detection uncertainty noise and false alarms the approach involves modelling the respective collections of targets and measurements as random finite sets and applying the probability hypothesis density phd recursion to propagate the posterior intensity which is a first order statistic of the random finite set of targets in time at present there is no closed form solution to the phd recursion this paper shows that under linear gaussian assumptions on the target dynamics and birth process the posterior intensity at any time step is a gaussian mixture more importantly closed form recursions for propagating the means covariances and weights of the constituent gaussian components of the posterior intensity are derived the proposed algorithm combines these recursions with a strategy for managing the number of gaussian components to increase efficiency this algorithm is extended to accommodate mildly nonlinear target dynamics using approximation strategies from the extended and unscented kalman filters

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

statistics of work performed on a forced quantum oscillator various aspects of the statistics of work performed by an external classical force on a quantum mechanical system are elucidated for a driven harmonic oscillator in this special case two parameters are introduced that are sufficient to completely characterize the force protocol explicit results for the characteristic function of work and the corresponding probability distribution are provided and discussed for three different types of initial states of the oscillator microcanonical canonical and coherent states depending on the choice of the initial state the probability distributions of the performed work may greatly differ this result in particular also holds true for identical force protocols general fluctuation and work theorems holding for microcanonical and canonical initial states are confirmed