energy dissipation and violation of the fluctuation response relation in nonequilibrium langevin systems the fluctuation response relation is a fundamental relation that is applicable to systems near equilibrium on the other hand when a system is driven far from equilibrium this relation is violated in general because the detailed balance condition is not satisfied in nonequilibrium systems even in this case it has been found that for a class of langevin equations there exists an equality between the extent of violation of the fluctuation response relation in the nonequilibrium steady state and the rate of energy dissipation from the system into the environment t harada and s i sasa phys rev lett 95 130602 2005 since this equality involves only experimentally measurable quantities it serves as a proposition to determine experimentally whether the system can be described by a langevin equation furthermore the contribution of each degree of freedom to the rate of energy dissipation can be determined based on this equality in this paper we present a comprehensive description on this equality and provide a detailed derivation for various types of models including many body systems brownian motor models time dependent systems and systems with multiple heat reservoirs

direct evaluation of large deviation functions we introduce a numerical procedure to evaluate directly the probabilities of large deviations of physical quantities such as current or density that are local in time the large deviation functions are given in terms of the typical properties of a modified dynamics and since they no longer involve rare events can be evaluated efficiently and over a wider ranges of values we illustrate the method with the current fluctuations of the totally asymmetric exclusion process and with the work distribution of a driven lorentz gas

nonconvexity of the relative entropy for markov dynamics a fisher information approach we show via counterexamples that relative entropy between the solution of a markovian master equation and the steady state is not a convex function of time we thus disprove the hypotheses that a general evolution principle of thermodynamics based on the decrease of the nonadiabatic entropy production could hold however we argue that a large separation of typical decay times is necessary for nonconvex solutions to occur making concave transients extremely short lived with respect to the main relaxation modes we describe a general method based on the fisher information matrix to discriminate between generators that admit nonconvex solutions and those that do not while initial conditions leading to concave transients are shown to be extremely fine tuned by our method we are able to select nonconvex initial conditions that are arbitrarily close to the steady state convexity does occur when the system is close to satisfying detailed balance or more generally when certain normality conditions of the decay modes are satisfied our results circumscribe the range of validity of a conjecture by maes et al phys rev lett 107 010601 2011 regarding monotonicity of the large deviation rate functional for the occupation probability showing that while the conjecture might hold in the long time limit the conditions for lyapunov s second criterion for stability are not met

nonequilibrium thermodynamics of stochastic systems with odd and even variables the total entropy production of stochastic systems can be divided into three quantities the first corresponds to the excess heat while the second two comprise the housekeeping heat we denote these two components the transient and generalized housekeeping heat and we obtain an integral fluctuation theorem for the latter valid for all markovian stochastic dynamics a previously reported formalism is obtained when the stationary probability distribution is symmetric for all variables that are odd under time reversal which restricts consideration of directional variables such as velocity

nonequilibrium equalities in absolutely irreversible processes we generalize nonequilibrium integral equalities to situations involving absolutely irreversible processes for which the forward path probability vanishes and the entropy production diverges rendering conventional integral fluctuation theorems inapplicable we identify the mathematical origins of absolute irreversibility as the singularity of probability measure we demonstrate the validity of the obtained equalities for several models

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

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

thermodynamic inference based on coarse grained data or noisy measurements fluctuation theorems have become an important tool in single molecule biophysics to measure free energy differences from nonequilibrium experiments when significant coarse graining or noise affect the measurements the determination of the free energies becomes challenging in order to address this thermodynamic inference problem we propose improved estimators of free energy differences based on fluctuation theorems which we test on a number of examples the effect of the noise can be described by an effective temperature which only depends on the signal to noise ratio when the work is gaussian distributed and uncorrelated with the error made on the work the notion of effective temperature appears less useful for non gaussian work distributions or when the error is correlated with the work but nevertheless as we show improved estimators can still be constructed for such cases as an example of nontrivial correlations between the error and the work we also consider measurements with delay as described by linear langevin equations

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

on adding a list of numbers and other one dependent determinantal processes adding a column of numbers produces carries along the way we show that random digits produce a pattern of carries with a neat probabilistic description the carries form a one dependent determinantal point process this makes it easy to answer natural questions how many carries are typical where are they located we show that many further examples from combinatorics algebra and group theory have essentially the same neat formulae and that any one dependent point process on the integers is determinantal the examples give a gentle introduction to the emerging fields of one dependent and determinantal point processes

best statistics of markovian fluxes a tale of eulerian tours and fermionic ghosts we provide an exact expression for the statistics of the fluxes of markov jump processes at all times improving on asymptotic results from large deviation theory the main ingredient is a generalization of the best theorem in enumeratoric graph theory to eulerian tours with open ends in the long time limit we reobtain sanov s theorem for markov processes which expresses the exponential suppression of fluctuations in terms of relative entropy the finite time power law term increasingly important with the system size is a spanning tree determinant that by introducing grassmann variables can be absorbed into the effective lagrangian of a fermionic ghost field on a metric space coupled to a gauge potential with reference to concepts in nonequilibrium stochastic thermodynamics the metric is related to the dynamical activity that measures net communication between states and the connection is made to a previous gauge theory for diffusion processes

integral fluctuation theorems for stochastic resetting systems we study the stochastic thermodynamics of resetting systems violation of microreversibility means that the well known derivations of fluctuations theorems break down for dynamics with resetting despite that we show that stochastic resetting systems satisfy two integral fluctuation theorems the first is the hatano sasa relation describing the transition between two steady states the second integral fluctuation theorem involves a functional that includes both dynamical and thermodynamic contributions we find that the second law like inequality found by fuchs et al for resetting systems europhys lett 113 60009 2016 euleej0295 507510 1209 0295 5075 113 60009 can be recovered from this integral fluctuation theorem with the help of jensen s inequality

the modified sutherland einstein relation for diffusive non equilibria there remains a useful relation between diffusion and mobility for a langevin particle in a periodic medium subject to non conservative forces the usual fluctuation dissipation relation can be easily modified and the mobility matrix is no longer proportional to the diffusion matrix with a correction term depending explicitly on the non equilibrium forces we discuss this correction by considering various simple examples and we visualize the various dependencies on the applied forcing and on the time by means of simulations for example in all cases the diffusion depends on the external forcing more strongly than does the mobility we also give an explicit decomposition of the symmetrized mobility matrix as the difference between two positive matrices one involving the diffusion matrix and the other involving force force correlations

low frequency asymptotic analysis of a string with rapidly oscillating density we consider the eigenvalue problem associated to the vibrations of a string with a rapidly oscillating bounded periodic density it is well known that when the size of the microstructure epsilon is small enough with respect to the wavelength of the eigenfunctions 1 sqrt lambda epsilon eigenvalues and eigenfunctions can be approximated by those of the limit system where the oscillating density is replaced by its average on the other hand it has been observed that when the size of the microstructure is of the order of the wavelength of the eigenfunctions epsilon sim 1 sqrt lambda epsilon singular phenomena may occur in this paper we study the behavior of the eigenvalues and eigenfunctions when 1 sqrt lambda epsilon approaches the critical size epsilon to do this we use the wkb approximation which allows us to find an explicit formula for eigenvalues and eigenfunctions with respect to epsilon in particular our analysis provides all order correction formulas fo

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

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

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

fluctuation theorem and large deviation function for a solvable model of a molecular motor we study a discrete stochastic model of a molecular motor this discrete model can be viewed as a minimal ratchet model we extend our previous work on this model by further investigating the constraints imposed by the fluctuation theorem on the operation of a molecular motor far from equilibrium in this work we show the connections between different formulations of the fluctuation theorem one formulation concerns the generating function of the currents while another one concerns the corresponding large deviation function which we have calculated exactly for this model a third formulation concerns the ratio of the probability of observing a velocity v to the same probability of observing a velocity ensuremath v finally we show that all the formulations of the fluctuation theorem can be understood from the notion of entropy production

macroscopic constraints for the minimum entropy production principle in an essential and quite general setup based on networks we identify schnakenberg s observables as the constraints that prevent a system from relaxing to equilibrium showing that in the linear regime steady states satisfy a minimum entropy production principle the result is applied to master equation systems opening a new path to a well known version of the principle regarding invariant states moreover with the aid of a simple example the principle is shown to conform to prigogine s original formulation finally we discuss analogies and differences with a recently proposed maximum entropy production principle

exact fluctuation theorem without ensemble quantities evaluating the entropy production ep along a stochastic trajectory requires the knowledge of the system probability distribution an ensemble quantity notoriously difficult to measure in this paper we show that the ep of nonautonomous systems in contact with multiple reservoirs can be expressed solely in terms of physical quantities measurable at the single trajectory level with a suitable preparation of the initial condition as a result we identify universal energy and particle fluctuation relations valid for any measurement time we apply our findings to an electronic junction model which may be used to verify our prediction experimentally

fluctuating currents in stochastic thermodynamics i gauge invariance of asymptotic statistics stochastic thermodynamics uses markovian jump processes to model random transitions between observable mesoscopic states physical currents are obtained from antisymmetric jump observables defined on the edges of the graph representing the network of states the asymptotic statistics of such currents are characterized by scaled cumulants in the present work we use the algebraic and topological structure of markovian models to prove a gauge invariance of the scaled cumulant generating function exploiting this invariance yields an efficient algorithm for practical calculations of asymptotic averages and correlation integrals we discuss how our approach generalizes the schnakenberg decomposition of the average entropy production rate and how it unifies previous work the application of our results to concrete models is presented in an accompanying publication

gallavotti cohen type symmetry related to cycle decompositions for markov chains and biochemical applications we slightly extend the fluctuation theorem obtained in lebowitz and spohn in j stat phys 95 333 365 1999 for sums of generators considering continuous time markov chains on a finite state space whose underlying graph has multiple edges and no loop this extended frame is suited when analyzing chemical systems as simple corollary we derive by a different method the fluctuation theorem of d andrieux and p gaspard for the fluxes along the chords associated to a fundamental set of oriented cycles andrieux and gaspard in j stat phys 127 107 131 2007

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

fluctuation theorem for currents and schnakenberg network theory a fluctuation theorem is proved for the macroscopic currents of a system in a nonequilibrium steady state by using schnakenberg network theory the theorem can be applied in particular in reaction systems where the affinities or thermodynamic forces are defined globally in terms of the cycles of the graph associated with the stochastic process describing the time evolution