first passage times in renewal and nonrenewal systems fluctuations in stochastic systems are usually characterized by full counting statistics which analyzes the distribution of the number of events taking place in the fixed time interval in an alternative approach the distribution of the first passage times i e the time delays after which the counting variable reaches a certain threshold value is studied this paper presents the approach to calculate the first passage time distribution in systems in which the analyzed current is associated with an arbitrary set of transitions within the markovian network using this approach it is shown that when the subsequent first passage times are uncorrelated there exist strict relations between the cumulants of the full counting statistics and the first passage time distribution on the other hand when the correlations of the first passage times are present their distribution may provide additional information about the internal dynamics of the system in comparison to the full counting statistics for example it may reveal the switching between different dynamical states of the system additionally i show that breaking of the fluctuation theorem for first passage times may reveal the multicyclic nature of the markovian network

unified approach to classical speed limit and thermodynamic uncertainty relation the total entropy production quantifies the extent of irreversibility in thermodynamic systems which is nonnegative for any feasible dynamics when additional information such as the initial and final states or moments of an observable is available it is known that tighter lower bounds on the entropy production exist according to the classical speed limits and the thermodynamic uncertainty relations here we obtain a universal lower bound on the total entropy production in terms of probability distributions of an observable in the time forward and backward processes for a particular case we show that our universal relation reduces to a classical speed limit imposing a constraint on the speed of the system s evolution in terms of the hatano sasa entropy production notably the obtained classical speed limit is tighter than the previously reported bound by a constant factor moreover we demonstrate that a generalized thermodynamic uncertainty relation can be derived from another particular case of the universal relation our uncertainty relation holds for systems with time reversal symmetry breaking and recovers several existing bounds our approach provides a unified perspective on two closely related classes of inequality classical speed limits and thermodynamic uncertainty relations

skewness and kurtosis in statistical kinetics we obtain lower and upper bounds on the skewness and kurtosis associated with the cycle completion time of unicyclic enzymatic reaction schemes analogous to a well known lower bound on the randomness parameter the lower bounds on skewness and kurtosis are related to the number of intermediate states in the underlying chemical reaction network our results demonstrate that evaluating these higher order moments with single molecule data can lead to information about the enzymatic scheme that is not contained in the randomness parameter

entropy production and kullback leibler divergence between stationary trajectories of discrete systems the irreversibility of a stationary time series can be quantified using the kullback leibler divergence kld between the probability of observing the series and the probability of observing the time reversed series moreover this kld is a tool to estimate entropy production from stationary trajectories since it gives a lower bound to the entropy production of the physical process generating the series in this paper we introduce analytical and numerical techniques to estimate the kld between time series generated by several stochastic dynamics with a finite number of states we examine the accuracy of our estimators for a specific example a discrete flashing ratchet and investigate how close the kld is to the entropy production depending on the number of degrees of freedom of the system that are sampled in the trajectories

multidimensional thermodynamic uncertainty relations we extend a class of recently derived thermodynamic uncertainty relations to vector valued observables in contrast to the scalar valued observables examined previously this multidimensional thermodynamic uncertainty relation provides a natural way to study currents in high dimensional systems and to obtain relations between different observables our proof is based on the generalized cramer rao inequality which we interpret as a relation between physical observables and the fisher information this allows us to develop high dimensional versions of both the original steady state uncertainty relation and the more recently obtained generalized uncertainty relation for time periodic systems we apply the multidimensional uncertainty relation to obtain a new constraint on the performance of steady state heat engines which is tighter than previous bounds and reveals the role of heat work correlations as a second application we show that the uncertainty relation is connected to a bound on the differential mobility as a result of this connection we find that a necessary condition for equality in the uncertainty relation is that the system obeys the equilibrium fluctuation dissipation relation

optimal cycles for low dissipation heat engines we consider the optimization of a finite time carnot engine characterized by small dissipations we bound the power with a simple inequality and show that the optimal strategy is to perform small cycles around a given working point which can be thus chosen optimally remarkably this optimal point is independent of the figure of merit combining power and efficiency that is being maximized furthermore for a general class of dissipative dynamics the maximal power output becomes proportional to the heat capacity of the working substance since the heat capacity can scale supraextensively with the number of constituents of the engine this enables us to design optimal many body carnot engines reaching maximum efficiency at finite power per constituent in the thermodynamic limit

a generalization of the thermodynamic uncertainty relation to periodically driven systems the thermodynamic uncertainty relation expresses a universal trade off between precision and entropy production which applies in its original formulation to current observables in steady state systems we generalize this relation to periodically time dependent systems and relatedly to a larger class of inherently time dependent current observables in the context of heat engines or molecular machines our generalization applies not only to the work performed by constant driving forces but also to the work performed while changing energy levels the entropic term entering the generalized uncertainty relation is the sum of local rates of entropy production which are modified by a factor that refers to an effective time independent probability distribution the conventional form of the thermodynamic uncertainty relation is recovered for a time independently driven steady state and additionally in the limit of fast driving we illustrate our results for a simple model of a heat engine with two energy levels

cayley differential unitary space time codes one method for communicating with multiple antennas is to encode the transmitted data differentially using unitary matrices at the transmitter and to decode differentially without knowing the channel coefficients at the receiver since channel knowledge is not required at the receiver differential schemes are ideal for use on wireless links where channel tracking is undesirable or infeasible either because of rapid changes in the channel characteristics or because of limited system resources although this basic principle is well understood it is not known how to generate good performing constellations of unitary matrices for any number of transmit and receive antennas and for any rate this is especially true at high rates where the constellations must be rapidly encoded and decoded we propose a class of cayley codes that works with any number of antennas and has efficient encoding and decoding at any rate the codes are named for their use of the cayley transform which maps the highly nonlinear stiefel manifold of unitary matrices to the linear space of skew hermitian matrices this transformation leads to a simple linear constellation structure in the cayley transform domain and to an information theoretic design criterion based on emulating a cauchy random matrix moreover the resulting cayley codes allow polynomial time near maximum likelihood ml decoding based on either successive nulling canceling or sphere decoding simulations show that the cayley codes allow efficient and effective high rate data transmission in multiantenna communication systems without knowing the channel

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

modulated two level system exact work statistics we consider an open two level system driven by a piecewise constant periodic field and described by a rate equation with fermi bose and arrhenius rates respectively we derive an analytical expression for the generating function and large deviation function of the work performed by the field and show that a work fluctuation theorem holds

canonical structure and orthogonality of forces and currents in irreversible markov chains we discuss a canonical structure that provides a unifying description of dynamical large deviations for irreversible finite state markov chains continuous time onsager theory and macroscopic fluctuation theory mft for markov chains this theory involves a non linear relation between probability currents and their conjugate forces within this framework we show how the forces can be split into two components which are orthogonal to each other in a generalised sense this splitting allows a decomposition of the pathwise rate function into three terms which have physical interpretations in terms of dissipation and convergence to equilibrium similar decompositions hold for rate functions at level 2 and level 2 5 these results clarify how bounds on entropy production and fluctuation theorems emerge from the underlying dynamical rules we discuss how these results for markov chains are related to similar structures within mft which describes hydrodynamic limits of such microscopic models

finite time generalization of the thermodynamic uncertainty relation for fluctuating currents in nonequilibrium steady states the recently discovered thermodynamic uncertainty relation expresses a fundamental relation between their variance and the overall entropic cost associated with the driving we show that this relation holds not only for the long time limit of fluctuations as described by large deviation theory but also for fluctuations on arbitrary finite time scales this generalization facilitates applying the thermodynamic uncertainty relation to single molecule experiments for which infinite time scales are not accessible importantly often this finite time variant of the relation allows inferring a bound on the entropy production that is even stronger than the one obtained from the long time limit we illustrate the relation for the fluctuating work that is performed by a stochastically switching laser tweezer on a trapped colloidal particle

arcsine laws in stochastic thermodynamics we show that the fraction of time that a thermodynamic current spends above its average value follows the arcsine law a prominent result obtained by levy for brownian motion stochastic currents with long streaks above or below their average are much more likely than those that spend similar fractions of time above and below their average our result is confirmed with experimental data from a brownian carnot engine we also conjecture that two other random times associated with currents obey the arcsine law the time a current reaches its maximum value and the last time a current crosses its average value these results apply to inter alia molecular motors quantum dots and colloidal systems

achieve higher efficiency at maximum power with finite time quantum otto cycle the optimization of heat engines was intensively explored to achieve higher efficiency while maintaining the output power however most investigations were limited to a few finite time cycles e g the carnot like cycle due to the complexity of the finite time thermodynamics in this paper we propose a class of finite time engine with quantum otto cycle and demonstrate a higher achievable efficiency at maximum power the current model can be widely utilized benefitting from the general c 2 scaling of extra work for a finite time adiabatic process with long control time we apply the adiabatic perturbation method to the quantum piston model and calculate the efficiency at maximum power which is validated with an exact solution

fluctuation theorem for partially masked nonequilibrium dynamics we establish a generalization of the fluctuation theorem for partially masked nonequilibrium dynamics we introduce a partial entropy production with a subset of all possible transitions and show that the partial entropy production satisfies the integral fluctuation theorem our result reveals the fundamental properties of a broad class of autonomous as well as nonautonomous nanomachines in particular our result gives a unified fluctuation theorem for both autonomous and nonautonomous maxwell s demons where mutual information plays a crucial role furthermore we derive a fluctuation dissipation theorem that relates nonequilibrium stationary current to two kinds of equilibrium fluctuations

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

effective fluctuation and response theory the so called fluctuation theorems pushed the study of systems far beyond equilibrium whose response to thermodynamic forces affinities is characterized by the reciprocal and the fluctuation dissipation relations all these results rely on the assumption that the observer has complete information about the system no hidden leakage to the environment exact evaluation of the thermodynamic cost of processes will an observer who has marginal information be able to perform an effective thermodynamic analysis given that such observer will only be able to establish local equilibrium by perturbing the stalling currents will he she observe equilibrium like fluctuations within the formalism of markov jump processes on finite networks we provide a broad theory of the statistical behavior of some out of many currents that flow across a system in particular 1 there exist effective affinities for which an integral fluctuation relation holds 2 at stalling i e where the marginal currents vanish a symmetrized fluctuation dissipation relation holds 3 under reasonable assumptions on the parametrization of the rates effective affinities can be operationally defined by a procedure of tuning to stalling 4 there exists a notion of marginally time reversed process which restores the full fledged fluctuation relation and reciprocity 5 there exist fluctuation relations across different levels in the hierarchy of more and more complete theories the above results apply to configuration space currents and to their phenomenological linear combinations provided certain symmetries of the effective affinities are respected a condition whose range of validity we deem the most interesting question left open to future inquiry

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

bound on thermoelectric power in a magnetic field within linear response for thermoelectric power generation in a multiterminal geometry strong numerical evidence for a universal bound as a function of the magnetic field induced asymmetry of the nondiagonal onsager coefficients is presented this bound implies inter alia that the power vanishes at least linearly when the maximal efficiency is approached in particular this result rules out that carnot efficiency can be reached at finite power which an analysis based on the second law only would in principle allow

structured unitary space time autocoding constellations we previously showed that arbitrarily reliable communication is possible within a single coherence interval in rayleigh flat fading as the symbol duration of the coherence interval and the number of transmit antennas grow simultaneously this effect where the space time signals act as their own channel codes is called autocoding for relatively short e g 16 symbol coherence intervals a codebook of independent isotropically random unitary space time signals theoretically supports transmission rates that are a significant fraction of autocapacity with an extremely low probability of error the exploitation of space time autocoding requires the creation and decoding of extraordinarily large constellations typically l 2 sup 80 we make progress on the first part of the problem through a random but highly structured constellation that is completely specified by log sub 2 l independent isotropically distributed unitary matrices the distinguishing property of this construction is that any two signals in the constellation are pairwise statistically independent and isotropically distributed thus the pairwise probability of error and hence the union bound on the block probability of error of the structured constellation is identical to that of a fully random constellation of independent signals we establish the limitations of an earlier construction through a subsidiary result that is interesting in its own right the square or for that matter any integer power greater than one of an isotropically random unitary matrix is not isotropically random with the sole exception of the one by one unitary matrix

characterizing dynamical transitions in bistable systems using a non equilibrium measurement of work abstract we show how the jarzynski relation can be exploited to analyze the nature of order disorder and a bifurcation type dynamical transition in terms of a response function derived on the basis of work distribution over non equilibrium paths between two thermalized states the validity of the response function extends over a linear as well as a nonlinear regime and far from equilibrium situations

large deviations of the current for driven periodic diffusions we study the large deviations of the time integrated current for a driven diffusion on the circle often used as a model of nonequilibrium systems we obtain the large deviation functions describing the current fluctuations using a fourier bloch decomposition of the so called tilted generator and we also construct from this decomposition the effective biased auxiliary or driven markov process describing the diffusion as current fluctuations are observed in time this effective process provides a clear physical explanation of the various fluctuation regimes observed it is used here to obtain an upper bound on the current large deviation function which we compare to a recently derived entropic bound and to study the low noise limit of large deviations

exact results for the finite time thermodynamic uncertainty relation we obtain exact results for the recently discovered finite time thermodynamic uncertainty relation for the dissipated work w d in a stochastically driven system with non gaussian work statistics

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

thermodynamic uncertainty relation for arbitrary initial states the thermodynamic uncertainty relation tur describes a trade off relation between nonequilibrium currents and entropy production and serves as a fundamental principle of nonequilibrium thermodynamics however currently known turs presuppose either specific initial states or an infinite time average which severely limits the range of applicability here we derive a finite time tur valid for arbitrary initial states from the cram er rao inequality we find that the variance of an accumulated current is bounded from below by the instantaneous current at the final time which suggests that the boundary is constrained by the bulk we apply our results to feedback controlled processes and successfully explain a recent experiment which reports a violation of a modified tur with feedback control we also derive a tur that is linear in the total entropy production and valid for discrete time markov chains with nonsteady initial states the obtained bound exponentially improves the existing bounds in a discrete time regime

on the design of layered space time systems for autocoding hochwald et al see ieee trans inform theory nov 2001 have recognized that arbitrarily reliable communication is possible in multiantenna systems with coding over only a single coherence interval in particular they showed that reliable communication is possible for all rates r spl les c sub a with code words that extend over a single coherence interval when the number of transmit antennas and coherence interval n t spl rarr spl infin they coined the names autocoding for this phenomenon and autocapacity for c sub a they also proposed a signalling scheme based on random unitary matrices that achieves a significant fraction of this capacity the main limitation however is that currently no decoder of reasonable complexity is known for this signalling scheme we investigate the application of space time layering to autocoding we show that properly constructed layered systems can achieve the autocapacity with a reasonable complexity receiver composed of minimum mean square error mmse decision feedback multiuser detectors and single user decoders in addition to this asymptotic result we propose a specific layering approach the threaded space time layering that combines generalized bit interleaved space time coded modulation iterative signal processing and pilot symbol assisted channel estimation we show that this approach is well suited for practical systems with limited numbers of transmit antennas and small coherence intervals finally we report simulation results that demonstrate the ability of the threaded approach to achieve significant fractions of the autocapacity with a realizable receiver the simulation results also indicate significant performance gains over the cayley differential space time signalling scheme in certain scenarios

equilibrium free energies from nonequilibrium measurements using maximum likelihood methods we present a maximum likelihood argument for the bennett acceptance ratio method and derive a simple formula for the variance of free energy estimates generated using this method this derivation of the acceptance ratio method using a form of logistic regression a common statistical technique allows us to shed additional light on the underlying physical and statistical properties of the method for example we demonstrate that the acceptance ratio method yields the lowest variance for any estimator of the free energy which is unbiased in the limit of large numbers of measurements

entropy production estimation with optimal current entropy production characterizes the thermodynamic irreversibility and reflects the amount of heat dissipated into the environment and free energy lost in nonequilibrium systems according to the thermodynamic uncertainty relation we propose a deterministic method to estimate the entropy production from a single trajectory of system states we explicitly and approximately compute an optimal current that yields the tightest lower bound using predetermined basis currents notably the obtained tightest lower bound is intimately related to the multidimensional thermodynamic uncertainty relation by proving the saturation of the thermodynamic uncertainty relation in the short time limit the exact estimate of the entropy production can be obtained for overdamped langevin systems irrespective of the underlying dynamics for markov jump processes because the attainability of the thermodynamic uncertainty relation is not theoretically ensured the proposed method provides the tightest lower bound for the entropy production when entropy production is the optimal current a more accurate estimate can be further obtained using the integral fluctuation theorem we illustrate the proposed method using three systems a four state markov chain a periodically driven particle and a multiple bead spring model the estimated results in all examples empirically verify the effectiveness and efficiency of the proposed method

efficiency versus speed in quantum heat engines rigorous constraint from lieb robinson bound a long standing open problem whether a heat engine with finite power achieves the carnot efficiency is investgated we rigorously prove a general trade off inequality on thermodynamic efficiency and time interval of a cyclic process with quantum heat engines in a first step employing the lieb robinson bound we establish an inequality on the change in a local observable caused by an operation far from support of the local observable this inequality provides a rigorous characterization of the following intuitive picture that most of the energy emitted from the engine to the cold bath remains near the engine when the cyclic process is finished using this description we prove an upper bound on efficiency with the aid of quantum information geometry our result generally excludes the possibility of a process with finite speed at the carnot efficiency in quantum heat engines in particular the obtained constraint covers engines evolving with non markovian dynamics which almost all previous studies on this topic fail to address

correlation decay and conformal anomaly in the two dimensional random bond ising ferromagnet the two dimensional random bond ising model is numerically studied on long strips by transfer matrix methods it is shown that the rate of decay of correlations at criticality as derived from averages of the two largest lyapunov exponents plus conformal invariance arguments differs from that obtained through direct evaluation of correlation functions the latter is found to be within error bars the same as in pure systems our results confirm field theoretical predictions the conformal anomaly c is calculated from the leading finite width correction to the averaged free energy on the strips estimates thus obtained are consistent with c 1 2 the same as for the pure ising model

stochastic thermodynamic interpretation of information geometry in recent years the unified theory of information and thermodynamics has been intensively discussed in the context of stochastic thermodynamics the unified theory reveals that information theory would be useful to understand nonstationary dynamics of systems far from equilibrium in this letter we have found a new link between stochastic thermodynamics and information theory well known as information geometry by applying this link an information geometric inequality can be interpreted as a thermodynamic uncertainty relationship between speed and thermodynamic cost we have numerically applied an information geometric inequality to a thermodynamic model of a biochemical enzyme reaction

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

tightening the uncertainty principle for stochastic currents we connect two recent advances in the stochastic analysis of nonequilibrium systems the loose uncertainty principle for the currents which states that statistical errors are bounded by thermodynamic dissipation and the analysis of thermodynamic consistency of the currents in the light of symmetries employing the large deviation techniques presented by gingrich et al phys rev lett 116 120601 2016 prltao0031 900710 1103 physrevlett 116 120601 and pietzonka barato and seifert phys rev e 93 052145 2016 2470 004510 1103 physreve 93 052145 we provide a short proof of the loose uncertainty principle and prove a tighter uncertainty relation for a class of thermodynamically consistent currents j our bound involves a measure of partial entropy production that we interpret as the least amount of entropy that a system sustaining current j can possibly produce at a given steady state we provide a complete mathematical discussion of quadratic bounds which allows one to determine which are optimal and finally we argue that the relationship for the fano factor of the entropy production rate var mean 2 is the most significant realization of the loose bound we base our analysis both on the formalism of diffusions and of markov jump processes in the light of schnakenberg s cycle analysis

integral fluctuation theorem for the housekeeping heat the housekeeping heat qhk is the dissipated heat necessary to maintain the violation of detailed balance in nonequilibrium steady states by analysing the evolution of its probability distribution we prove an integral fluctuation theorem exp qhk 1 valid for arbitrary driven transitions between steady states we discuss gaussian limiting cases and the difference between the new theorem and both the hatano sasa and the jarzynski relation

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

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

histories of adiabatic quantum transitions the way in which the transition amplitude to an initially unoccupied state increases to its exponentially small final value is studied in detail in the adiabatic approximation for a 2 state quantum system by transforming to a series of superadiabatic bases clinging ever closer to the exact evolving state it is shown that transition histories renormalize onto a universal one in which the amplitude grows to its final value as an error function rather than via large oscillations as in the ordinary adiabatic basis the time for the universal transition is of order surd hslash delta where delta is the small adiabatic slowness parameter in perturbation theory the pre exponential factor of the final amplitude renormalizes superadiabatically from the incorrect value textstyle frac 1 3 pi for the ordinary adiabatic basis to the correct value unity the various histories could be observed in spin experiments

universal bounds on current fluctuations for current fluctuations in nonequilibrium steady states of markovian processes we derive four different universal bounds valid beyond the gaussian regime different variants of these bounds apply to either the entropy change or any individual current e g the rate of substrate consumption in a chemical reaction or the electron current in an electronic device the bounds vary with respect to their degree of universality and tightness a universal parabolic bound on the generating function of an arbitrary current depends solely on the average entropy production a second stronger bound requires knowledge both of the thermodynamic forces that drive the system and of the topology of the network of states these two bounds are conjectures based on extensive numerics an exponential bound that depends only on the average entropy production and the average number of transitions per time is rigorously proved this bound has no obvious relation to the parabolic bound but it is typically tighter further away from equilibrium an asymptotic bound that depends on the specific transition rates and becomes tight for large fluctuations is also derived this bound allows for the prediction of the asymptotic growth of the generating function even though our results are restricted to networks with a finite number of states we show that the parabolic bound is also valid for three paradigmatic examples of driven diffusive systems for which the generating function can be calculated using the additivity principle our bounds provide a general class of constraints for nonequilibrium systems

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

optimization induced by stability and the role of limited control near a steady state a relationship between stability and self optimization is found for weakly dissipative heat devices the effect of limited control on operation variables around an steady state is such that after instabilities the paths toward relaxation are given by trajectories stemming from restitution forces which improve the system thermodynamic performance power output efficiency and entropy generation statistics over random trajectories for many cycles shows this behavior as well two types of dynamics are analyzed one where an stability basin appears and another one where the system is globally stable under both dynamics there is an induced trend in the control variables space due to stability in the energetic space this behavior translates into a preference for better thermodynamic states and thus stability could favor self optimization under limited control this is analyzed from the multiobjective optimization perspective as a result the statistical behavior of the system is strongly influenced by the pareto front the set of points with the best compromise between several objective functions and the stability basin additionally endoreversible and irreversible behaviors appear as very relevant limits the first one is an upper bound in energetic performance connected with the pareto front and the second one represents an attractor for the stochastic trajectories

self consistent scaling theory for logarithmic correction exponents multiplicative logarithmic corrections frequently characterize critical behavior in statistical physics here a recently proposed theory relating the exponents of such terms is extended to account for circumstances which often occur when the leading specific heat critical exponent vanishes also the theory is widened to encompass the correlation function the new relations are then confronted with results from the literature and some new predictions for logarithmic corrections in certain models are made

space time autocoding prior treatments of space time communications in rayleigh flat fading generally assume that channel coding covers either one fading interval in which case there is a nonzero outage capacity or multiple fading intervals in which case there is a nonzero shannon capacity however we establish conditions under which channel codes span only one fading interval and yet are arbitrarily reliable in short space time signals are their own channel codes we call this phenomenon space time autocoding and the accompanying capacity the space time autocapacity let an m transmitter antenna n receiver antenna rayleigh flat fading channel be characterized by an m spl times n matrix of independent propagation coefficients distributed as zero mean unit variance complex gaussian random variables this propagation matrix is unknown to the transmitter it remains constant during a t symbol coherence interval and there is a fixed total transmit power let the coherence interval and number of transmitter antennas be related as t spl beta m for some constant spl beta a t spl times m matrix valued signal associated with r spl middot t bits of information for some rate r is transmitted during the t symbol coherence interval then there is a positive space time autocapacity c sub a such that for all r c sub a the block probability of error goes to zero as the pair t m spl rarr spl infin such that t m spl beta the autocoding effect occurs whether or not the propagation matrix is known to the receiver and c sub a nlog 1 spl rho in either case independently of spl beta where spl rho is the expected signal to noise ratio snr at each receiver antenna lower bounds on the cutoff rate derived from random unitary space time signals suggest that the autocoding effect manifests itself for relatively small values of t and m for example within a single coherence interval of duration t 16 for m 7 transmitter antennas and n 4 receiver antennas and an 18 db expected snr a total of 80 bits corresponding to rate r 5 can theoretically be transmitted with a block probability of error less than 10 sup 9 all without any training or knowledge of the propagation matrix

logarithmic corrections to gap scaling in random bond ising strips numerical results for the first gap of the lyapunov spectrum of the self dual random bond ising model on strips are analysed it is shown that finite width corrections can be fitted very well by an inverse logarithmic form predicted to hold when the hamiltonian contains a marginal operator

inferring entropy production from short experiments we provide a strategy for the exact inference of the average as well as the fluctuations of the entropy production in nonequilibrium systems in the steady state from the measurements of arbitrary current fluctuations our results are built upon the finite time generalization of the thermodynamic uncertainty relation and require only very short time series data from experiments we illustrate our results with exact and numerical solutions for two colloidal heat engines

a gallavotti cohen evans morriss like symmetry for a class of markov jump processes we investigate a new symmetry of the large deviation function of certain time integrated currents in non equilibrium systems the symmetry is similar to the well known gallavotti cohen evans morriss symmetry for the entropy production but it concerns a different functional of the stochastic trajectory the symmetry can be found in a restricted class of markov jump processes where the network of microscopic transitions has a particular structure and the transition rates satisfy certain constraints we provide three physical examples where time integrated observables display such a symmetry moreover we argue that the origin of the symmetry can be traced back to time reversal if stochastic trajectories are grouped appropriately

large deviation function for entropy production in driven one dimensional systems the large deviation function for entropy production is calculated by solving a time independent eigenvalue problem for a particle driven along a periodic potential in an intermediate force regime the large deviation function shows pronounced deviations from a gaussian behavior with a characteristic kink at zero entropy production such a feature can also be extracted from the analytical solution of the asymmetric random walk to which the driven particle can be mapped in a certain parameter range

universal trade off relation between power and efficiency for heat engines for a general thermodynamic system described as a markov process we prove a general lower bound for dissipation in terms of the square of the heat current thus establishing that nonvanishing current inevitably implies dissipation this leads to a universal trade off relation between efficiency and power with which we rigorously prove that a heat engine with nonvanishing power never attains the carnot efficiency our theory applies to systems arbitrarily far from equilibrium and does not assume any specific symmetry of the model

uncertainty relations in stochastic processes an information inequality approach the thermodynamic uncertainty relation is an inequality stating that it is impossible to attain higher precision than the bound defined by entropy production in statistical inference theory information inequalities assert that it is infeasible for any estimator to achieve an error smaller than the prescribed bound inspired by the similarity between the thermodynamic uncertainty relation and the information inequalities we apply the latter to systems described by langevin equations and we derive the bound for the fluctuation of thermodynamic quantities when applying the cram er rao inequality the obtained inequality reduces to the fluctuation response inequality we find that the thermodynamic uncertainty relation is a particular case of the cram er rao inequality in which the fisher information is the total entropy production using the equality condition of the cram er rao inequality we find that the stochastic total entropy production is the only quantity that can attain equality in the thermodynamic uncertainty relation furthermore we apply the chapman robbins inequality and obtain a relation for the lower bound of the ratio between the variance and the sensitivity of systems in response to arbitrary perturbations

leveraging coherent space time codes for noncoherent communication via training training codes are introduced for the multiple antenna noncoherent multiple block rayleigh fading channel in which the fading coefficients which are constant over a fixed number of dimensions coherence interval for each block and then change independently to a new realization are known neither at the transmitter nor at the receiver each codeword of a training code consists of a part known to the receiver used to form a minimum mean squared error mmse estimate of the channel and a part that contains codeword s of a space time block or trellis code designed for the coherent channel in which the receiver has perfect knowledge of the channel the channel estimate is used as if it were error free for decoding the information bearing part of the training codeword training codes are hence easily designed to have high rate and low decoding complexity by choosing the underlying coherent code to have high rate and to be efficiently decodable conditions for which the estimator detector e d receiver is equivalent to the optimal noncoherent receiver are established a key performance analysis result of this paper is that the training codes when decoded with the e d receiver achieve a diversity order of the error probability that is equal to the diversity order of the underlying coherent code in some cases the performance of training codes can be measured relative to coherent reception via training efficiency which is then optimized over the energy allocation between the training and data phases in the limit of increasing block lengths training codes always achieve the performance of coherent reception the examples of training codes provided in this work have polynomial complexity in rate but an error rate comparable to the best performing unitary designs available even though the latter require exponential decoding complexity

proof of the finite time thermodynamic uncertainty relation for steady state currents this paper presents the finite time version of the thermodynamic uncertainty relation for nonequilibrium steady states which sets a bound on the magnitude of current fluctuations the authors use a methodology that is similar to the proof for the long time limit but with large deviation theory applied to an ensemble of many copies

frenetic bounds on the entropy production we give a systematic derivation of positive lower bounds for the expected entropy production ep rate in classical statistical mechanical systems obeying a dynamical large deviation principle the logic is the same for the return to thermodynamic equilibrium as it is for steady nonequilibria working under the condition of local detailed balance we recover there recently studied uncertainty relations for the ep appearing in studies about the effectiveness of mesoscopic machines in general our refinement of the positivity of the expected ep rate is obtained in terms of a positive and even function of the expected current s which measures the dynamical activity in the system a time symmetric estimate of the changes in the system s configuration also underdamped diffusions can be included in the analysis

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

large fluctuations of the macroscopic current in diffusive systems a numerical test of the additivity principle most systems when pushed out of equilibrium respond by building up currents of locally conserved observables understanding how microscopic dynamics determines the averages and fluctuations of these currents is one of the main open problems in nonequilibrium statistical physics the additivity principle is a theoretical proposal that allows to compute the current distribution in many one dimensional nonequilibrium systems using simulations we validate this conjecture in a simple and general model of energy transport both in the presence of a temperature gradient and in canonical equilibrium in particular we show that the current distribution displays a gaussian regime for small current fluctuations as prescribed by the central limit theorem and non gaussian exponential tails for large current deviations obeying in all cases the gallavotti cohen fluctuation theorem in order to facilitate a given current fluctuation the system adopts a well defined temperature profile different from that of the steady state and in accordance with the additivity hypothesis predictions system statistics during a large current fluctuation is independent of the sign of the current which implies that the optimal profile as well as higher order profiles and spatial correlations are invariant upon current inversion we also demonstrate that finite time joint fluctuations of the current and the profile are well described by the additivity functional these results suggest the additivity hypothesis as a general and powerful tool to compute current distributions in many nonequilibrium systems

simple bounds on fluctuations and uncertainty relations for first passage times of counting observables recent large deviation results have provided general lower bounds for the fluctuations of time integrated currents in the steady state of stochastic systems a corollary are so called thermodynamic uncertainty relations connecting precision of estimation to average dissipation here we consider this problem but for counting observables i e trajectory observables which in contrast to currents are non negative and nondecreasing in time and possibly symmetric under time reversal in the steady state their fluctuations to all orders are bound from below by a conway maxwell poisson distribution dependent only on the averages of the observable and of the dynamical activity we show how to obtain the corresponding bounds for first passage times times when a certain value of the counting variable is first reached and their uncertainty relations just like entropy production does for currents dynamical activity controls the bounds on fluctuations of counting observables

field theoretic thermodynamic uncertainty relation general formulation exemplified with the kardar parisi zhang equation we propose a field theoretic thermodynamic uncertainty relation as an extension of the one derived so far for a markovian dynamics on a discrete set of states and for overdamped langevin equations we first formulate a framework which describes quantities like current entropy production and diffusivity in the case of a generic field theory we will then apply this general setting to the one dimensional kardar parisi zhang equation a paradigmatic example of a non linear field theoretic langevin equation in particular we will treat the dimensionless kardar parisi zhang equation with an effective coupling parameter measuring the strength of the non linearity it will be shown that a field theoretic thermodynamic uncertainty relation holds up to second order in a perturbation expansion with respect to a small effective coupling constant the calculations show that the field theoretic variant of the thermodynamic uncertainty relation is not saturated for the case of the kardar parisi zhang equation due to an excess term stemming from its non linearity

direct evaluation of dynamical large deviation rate functions using a variational ansatz we describe a simple form of importance sampling designed to bound and compute large deviation rate functions for time extensive dynamical observables in continuous time markov chains we start with a model defined by a set of rates and a time extensive dynamical observable we construct a reference model a variational ansatz for the behavior of the original model conditioned on atypical values of the observable direct simulation of the reference model provides an upper bound on the large deviation rate function associated with the original model an estimate of the tightness of the bound and if the ansatz is chosen well the exact rate function the exact rare behavior of the original model does not need to be known in advance we use this method to calculate rate functions for currents and counting observables in a set of network and lattice models taken from the literature straightforward ansatze yield bounds that are tighter than bounds obtained from level 2 5 of large deviations via approximations that involve uniform scalings of rates we show how to correct these bounds in order to recover the rate functions exactly our approach is complementary to more specialized methods and offers a physically transparent framework for approximating and calculating the likelihood of dynamical large deviations