Fluctuations and Response of Nonequilibrium States (original) (raw)
Finite-temperature critical point of a glass transition
Proceedings of The National Academy of Sciences, 2010
We generalize the simplest kinetically constrained model of a glass-forming liquid by softening kinetic constraints, allowing them to be violated with a small finite rate. We demonstrate that this model supports a first-order dynamical (space-time) phase transition, similar to those observed with hard constraints. In addition, we find that the first-order phase boundary in this softened model ends in a finite-temperature dynamical critical point, which we expect to be present in natural systems. We discuss links between this critical point and quantum phase transitions, showing that dynamical phase transitions in ddd dimensions map to quantum transitions in the same dimension, and hence to classical thermodynamic phase transitions in d+1d+1d+1 dimensions. We make these links explicit through exact mappings between master operators, transfer matrices, and Hamiltonians for quantum spin chains.
Rings in random environments: sensing disorder through topology
Soft Matter, 2015
In this paper we study the role of topology in DNA gel electrophoresis experiments via molecular dynamics simulations. The gel is modelled as a 3D array of obstacles from which half edges are removed at random with probability p, thereby generating a disordered environment. Changes in the microscopic structure of the gel are captured by measuring the electrophoretic mobility of ring polymers moving through the medium, while their linear counterparts provide a control system as we show they are insensitive to these changes. We show that ring polymers provide a novel noninvasive way of exploiting topology to sense microscopic disorder. Finally, we compare the results from the simulations with an analytical model for the non-equilibrium differential mobility, and find a striking agreement between simulation and theory.
Two Refreshing Views of Fluctuation Theorems Through Kinematics Elements and Exponential Martingale
Journal of Statistical Physics, 2011
In the context of Markov evolution, we present two original approaches to obtain Generalized Fluctuation-Dissipation Theorems (GFDT), by using the language of stochastic derivatives and by using a family of exponential martingales functionals. We show that GFDT are perturbative versions of relations verified by these exponential martingales. Along the way, we prove GFDT and Fluctuation Relations (FR) for general Markov processes, beyond the usual proof for diffusion and pure jump processes. Finally, we relate the FR to a family of backward and forward exponential martingales.
Physical Review Letters, 2012
We discuss the consequences of a variant of the Hatano-Sasa relation in which a non-stationary distribution is used in place of the usual stationary one. We first show that this non-stationary distribution is related to a difference of traffic between the direct and dual dynamics. With this formalism, we extend the definition of the adiabatic and non-adiabatic entropies introduced by M. Esposito and C. Van den Broeck in Phys. Rev. Lett. 104, 090601 (2010) for the stationary case. We also obtain interesting second-law like inequalities for transitions between non-stationary states.
Fluctuation-Response Theorem for the Active Noisy Oscillator of the Hair-Cell Bundle
Physical Review Letters, 2012
The hair bundle of sensory cells in the vertebrate ear provides an example of a noisy oscillator close to a Hopf bifurcation. The analysis of the data from both spontaneous and forced oscillations shows a strong violation of the fluctuation-dissipation theorem, revealing the presence of an underlying active process that keeps the system out of equilibrium. Nevertheless, we show that a generalized fluctuation-dissipation theorem, valid for non-equilibrium steady states, is fulfilled within the limits of our experimental accuracy and computational approximations, when the adequate conjugate degrees of freedom are chosen.
Stochastic thermodynamics of active Brownian particles
Physical Review E, 2013
Examples of self propulsion in strongly fluctuating environment is abound in nature, e.g., molecular motors and pumps operating in living cells. Starting from Langevin equation of motion, we develop a stochastic thermodynamic description of non-interacting self propelled particles using simple models of velocity dependent forces. We derive fluctuation theorems for entropy production and a modified fluctuation dissipation relation, characterizing the linear response at non-equilibrium steady states. We study these notions in a simple model of molecular motors, and in the Rayleigh-Helmholtz and energy-depot model of self propelled particles.
Physical Review E, 2010
We discuss the relation between the fluctuation-dissipation relation derived by Chatelain and Ricci-Tersenghi [C.Chatelain, J.Phys. A 36, 10739 (2003); F. Ricci-Tersenghi, Phys.Rev.E 68, 065104(R) (2003)] and that by Lippiello-Corberi-Zannetti [E. Lippiello, F. Corberi and M. Zannetti Phys. Rev. E 71, 036104 (2005)]. In order to do that, we re-derive the fluctuation-dissipation relation for systems of discrete variables evolving in discrete time via a stochastic non-equilibrium Markov process. The calculation is carried out in a general formalism comprising the Chatelain, Ricci-Tersenghi result and that by Lippiello-Corberi-Zannetti as special cases. The applicability, generality, and experimental feasibility of the two approaches is thoroughly discussed. Extending the analytical calculation to the variance of the response function we show the vantage of field-free numerical methods with respect to the standard method where the perturbation is applied. We also show that the signal to noise ratio is better (by a factor √ 2) in the algorithm of Lippiello-Corberi-Zannetti with respect to that of Chatelain-Ricci Tersenghi. PACS: 05.70.Ln, 75.40.Gb, 05.40.-a I. INTRODUCTION
Nonequilibrium Fluctuation-Dissipation Theorem and Heat Production
Physical Review Letters, 2014
We use a relationship between response and correlation function in nonequilibrium systems to establish a connection between the heat production and the deviations from the equilibrium fluctuation-dissipation theorem. This scheme extends the Harada-Sasa formulation [Phys. Rev. Lett. 95, 130602 (2005)], obtained for Langevin equations in steady states, as it also holds for transient regimes and for discrete jump processes involving small entropic changes. Moreover, a general formulation includes two times and the new concepts of two-time work, kinetic energy, and of a two-time heat exchange that can be related to a nonequilibrium "effective temperature". Numerical simulations of a chain of anharmonic oscillators and of a model for a molecular motor driven by ATP hydrolysis illustrate these points.
Microscopic Theory for Negative Differential Mobility in Crowded Environments
Physical Review Letters, 2014
We study the behavior of the stationary velocity of a driven particle in an environment of mobile hard-core obstacles. Based on a lattice gas model, we demonstrate analytically that the drift velocity can exhibit a nonmonotonic dependence on the applied force, and show quantitatively that such negative differential mobility (NDM), observed in various physical contexts, is controlled by both the density and diffusion time scale of obstacles. Our study unifies recent numerical and analytical results obtained in specific regimes, and makes it possible to determine analytically the region of the full parameter space where NDM occurs. These results suggest that NDM could be a generic feature of biased (or active) transport in crowded environments.
Chemical Sensing by Nonequilibrium Cooperative Receptors
Physical Review Letters, 2013
Cooperativity arising from local interactions in equilibrium receptor systems provides gain, but does not increase sensory performance, as measured by the signal-to-noise ratio (SNR) due to a fundamental tradeoff between gain and intrinsic noise. Here we allow sensing to be a nonequilibrium process and show that energy dissipation cannot circumvent the fundamental tradeoff, so that SNR is still optimal for independent receptors. For systems requiring high gain, nonequilibrium 2D-coupled receptors maximize SNR, revealing a new design principle for biological sensors.
An update on the nonequilibrium linear response
New Journal of Physics, 2013
The unique fluctuation-dissipation theorem for equilibrium stands in contrast with the wide variety of nonequilibrium linear response formulae. Their most traditional approach is "analytic", which, in the absence of detailed balance, introduces the logarithm of the stationary probability density as observable. The theory of dynamical systems offers an alternative with a formula that continues to work when the stationary distribution is not smooth. We show that this method works equally well for stochastic dynamics, and we illustrate it with a numerical example for the perturbation of circadian cycles. A second "probabilistic" approach starts from dynamical ensembles and expands the probability weights on path space. This line suggests new physical questions, as we meet the frenetic contribution to linear response, and the relevance of the change in dynamical activity in the relaxation to a (new) nonequilibrium condition. PACS numbers: 05.70.Ln, 05.40.-a, 05.20.-y An update on nonequilibrium linear response
Thermal response in driven diffusive systems
The European Physical Journal B, 2014
Evaluating the linear response of a driven system to a change in environment temperature(s) is essential for understanding thermal properties of nonequilibrium systems. The system is kept in weak contact with possibly different fast relaxing mechanical, chemical or thermal equilibrium reservoirs. Modifying one of the temperatures creates both entropy fluxes and changes in dynamical activity. That is not unlike mechanical response of nonequilibrium systems but the extra difficulty for perturbation theory via path-integration is that for a Langevin dynamics temperature also affects the noise amplitude and not only the drift part. Using a discrete-time mesh adapted to the numerical integration one avoids that ultraviolet problem and we arrive at a fluctuation expression for its thermal susceptibility. The algorithm appears stable under taking even finer resolution. PACS. 05.70.Ln Nonequilibrium and irreversible thermodynamics -05.20.-y Classical statistical mechanics -05.10.Gg Stochastic analysis methods -05.40.Jc Brownian motion arXiv:1409.3369v1 [cond-mat.stat-mech]
Frenetic aspects of second order response
Phys. Chem. Chem. Phys., 2015
Starting from second order around thermal equilibrium, the response of a statistical mechanical system to an external stimulus is not only governed by dissipation and depends explicitly on dynamical details of the system. The so called frenetic contribution in second order around equilibrium is illustrated in different physical examples, such as for non-thermodynamic aspects in the coupling between system and reservoir, for the dependence on disorder in dielectric response and for the nonlinear correction to the Sutherland-Einstein relation. Inversely, systems or particles with different friction, reactivity, couplings or other kinetic features when in contact with an equilibrium reservoir can be distinguished and possibly separated in nonlinear response. * Electronic address: urna.basu@fys.kuleuven.be † Electronic address: mkrueger@is.mpg.de
Fluctuations and response from a Hatano and Sasa approach
Physica Scripta, 2012
In this commentary paper, we present some of the main ideas on deriving a modified fluctuation-dissipation theorem off equilibrium, which in the end can all be related to an approach based on a generalized Hatano-Sasa relation. This generalized Hatano-Sasa relation also contains an interesting inequality, which can be viewed as a generalization of the second law of thermodynamics to transitions between non-equilibrium states.
Physical Review E, 2012
We present a general framework for systems which are prepared in a non-stationary nonequilibrium state in the absence of any perturbation, and which are then further driven through the application of a time-dependent perturbation. We distinguish two different situations depending on the way the non-equilibrium state is prepared, either it is created by some driving; or it results from a relaxation following some initial non-stationary conditions. Our approach is based on a recent generalization of the Hatano-Sasa relation for non-stationary probability distributions.
Thermodynamic Transformations of Nonequilibrium States
Journal of Statistical Physics, 2012
We consider a macroscopic system in contact with boundary reservoirs and/or under the action of an external field. We discuss the case in which the external forcing depends explicitly on time and drives the system from a nonequilibrium state to another one. In this case the amount of energy dissipated along the transformation becomes infinite when an unbounded time window is considered. Following the general proposal by Oono and Paniconi and using results of the macroscopic fluctuation theory, we give a natural definition of a renormalized work. We then discuss its thermodynamic relevance by showing that it satisfies a Clausius inequality and that quasi static transformations minimize the renormalized work. In addition, we connect the renormalized work to the quasi potential describing the fluctuations in the stationary nonequilibrium ensemble. The latter result provides a characterization of the quasi potential that does not involve rare fluctuations.
Physical Review Letters, 2010
We derive the generalized Markovian description for the non-equilibrium Brownian motion of a heated particle in a simple solvent with a temperature-dependent viscosity. Our analytical results for the generalized fluctuation-dissipation and Stokes-Einstein relations compare favorably with measurements of laser-heated gold nano-particles and provide a practical rational basis for emerging photothermal technologies.
Nonequilibrium Linear Response for Markov Dynamics, II: Inertial Dynamics
Journal of Statistical Physics, 2010
Systems out of equilibrium, in stationary as well as in nonstationary regimes, display a linear response to energy impulses simply expressed as the sum of two specific temporal correlation functions. There is a natural interpretation of these quantities. The first term corresponds to the correlation between observable and excess entropy flux yielding a relation with energy dissipation like in equilibrium. The second term comes with a new meaning: it is the correlation between the observable and the excess in dynamical activity or reactivity, playing an important role in dynamical fluctuation theory out-of-equilibrium. It appears as a generalized escape rate in the occupation statistics. The resulting response formula holds for all observables and allows direct numerical or experimental evaluation, for example in the discussion of effective temperatures, as it only involves the statistical averaging of explicit quantities, e.g. without needing an expression for the nonequilibrium distribution. The physical interpretation and the mathematical derivation are independent of many details of the dynamics, but in this first part they are restricted to Markov jump processes and overdamped diffusions.
The modified Sutherland-Einstein relation for diffusive non-equilibria
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2011
There remains a useful relation between diffusion and mobility for a Langevin particle in a periodic medium subject to nonconservative forces. The usual fluctuation-dissipation relation easily gets modified and the mobility matrix is no longer proportional to the diffusion matrix, with a correction term depending explicitly on the (nonequilibrium) 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, the other force-force correlations. arXiv:1101.3227v2 [cond-mat.stat-mech]
Physical Review E, 2010
The definition of a nonequilibrium temperature through generalized fluctuation-dissipation relations relies on the independence of the fluctuation-dissipation temperature from the observable considered. We argue that this observable independence is deeply related to the uniformity of the phase-space probability distribution on the hypersurfaces of constant energy. This property is shown explicitly on three different stochastic models, where observable-dependence of the fluctuationdissipation temperature arises only when the uniformity of the phase-space distribution is broken. The first model is an energy transport model on a ring, with biased local transfer rules. In the second model, defined on a fully connected geometry, energy is exchanged with two heat baths at different temperatures, breaking the uniformity of the phase-space distribution. Finally, in the last model, the system is connected to a zero temperature reservoir, and preserves the uniformity of the phase-space distribution in the relaxation regime, leading to an observable-independent temperature.
Dependence of the Fluctuation-Dissipation Temperature on the Choice of Observable
Physical Review Letters, 2009
On general grounds, a nonequilibrium temperature can be consistently defined from generalized fluctuation-dissipation relations only if it is independent of the observable considered. We argue that the dependence on the choice of observable generically occurs when the phase-space probability distribution is non-uniform on constant energy shells. We relate quantitatively this observable dependence to a fundamental characteristics of nonequilibrium systems, namely the Shannon entropy difference with respect to the equilibrium state with the same energy. This relation is illustrated on a mean-field model in contact with two heat baths at different temperatures. 05.70.Ln, 05.10.Cc Characterizing nonequilibrium states through generalized, or effective, thermodynamic parameters is one of the important open issues in nonequilibrium statistical physics [1]. One possible approach is to introduce thermodynamic parameters conjugated to conserved quantities . An alternative approach, more suitable for the definition of temperatures, is to generalize the fluctuation-dissipation relations (FDR) that relate the linear response to an external perturbing field with the correlation of spontaneous fluctuations . At equilibrium, the proportionality coefficient is precisely the temperature. In nonequilibrium situations, one may use the ratio between correlation and response as a definition of a non-equilibrium temperature, as proposed in the context of hydrodynamic turbulence [5], spin-glasses [6-8], granular materials [9-11], or sheared fluids . The FDR approach is particularly useful since it allows for experimental and numerical measurements. A necessary condition for a consistent definition of a FDRbased temperature is that its value does not depend on the choice of observables underlying the FDR. For glassy systems, it has been shown that no dependence on the observable appears at the mean-field level . This property was also reported in numerical tests on more realistic models , although the conclusions may depend on the model considered . For non-glassy systems driven into a nonequilibrium steady-state, the situation remains unclear, and no generic conclusion has been reached, even though a lot of work has been devoted to the study of generalized FDR . Theoretical arguments on the observable dependence of the FDR-temperature are thus highly desirable.
Active Brownian particles: Entropy production and fluctuation response
Physical Review E, 2014
Within the Rayleigh-Helmholtz model of active Brownian particles activity is due to a non-linear velocity dependent force. In the presence of external trapping potential or constant force, the steady state of the system breaks detailed balance producing a net entropy. Using molecular dynamics simulations, we obtain the probability distributions of entropy production in these steady states. The distribution functions obey fluctuation theorems for entropy production. Using the simulation, we further show that the steady state response function obeys a modified fluctuation-dissipation relation.
Metastable states and space-time phase transitions in a spin-glass model
Physical Review E, 2010
We study large deviations of the dynamical activity in the random orthogonal model (ROM). This is a fully connected spin-glass model with one-step replica symmetry breaking behaviour, consistent with the random first-order transition scenario for structural glasses. We show that this model displays dynamical (space-time) phase-transitions between active and inactive phases, as demonstrated by singularities in large deviation functions. We argue that such transitions are generic in systems with long-lived metastable states.
Stochastic Energetics for Non-Gaussian Processes
Physical Review Letters, 2012
By introducing a new stochastic integral, we investigate the energetics of classical stochastic systems driven by non-Gaussian white noises. In particular, we introduce a decomposition of the total-energy difference into the work and the heat for each trajectory, and derive a formula to calculate the heat from experimental data on the dynamics. We apply our formulation and results to a Langevin system driven by a Poisson noise.
Coarse-grained second-order response theory
2020
While linear response theory, manifested by the fluctuation dissipation theorem, can be applied on any length scale, nonlinear response theory is fundamentally of microscopic nature. We develop an exact theoretical framework for analyzing nonlinear (second order) response of coarse grained observables to time-dependent perturbations, using a path-integral formalism. The resulting expressions involve correlations of the observable with coarse grained path weights. The time symmetric part of these weights depends on paths and perturbation protocol in a complex manner, and, furthermore, the absence of Markovianity prevents slicing of the coarse grained path integral. Despite this, we show that the response function can be expressed in terms of path weights corresponding to a single-step perturbation. This formalism thus leads to an extrapolation scheme, which circumvents the mentioned difficulties, and where measuring linear responses of coarse-grained variables suffices to determine t...
2020
The spontaneously oscillating hair bundle of sensory cells in the inner ear is an example of a stochastic, nonlinear oscillator driven by internal active processes. Moreover, this internal activity is adaptive -- its power input depends on the current state of the system. We study fluctuation dissipation relations in such adaptively-driven, nonequilibrium limit-cycle oscillators. We observe the expected violation of the well-known, equilibrium fluctuation-dissipation theorem (FDT), and verify the existence of a generalized fluctuation-dissipation theorem (GFDT) in the non-adaptively driven model of the hair cell oscillator. This generalized fluctuation theorem requires the system to be analyzed in the co-moving frame associated with the mean limit cycle of the stochastic oscillator. We then demonstrate, via numerical simulations and analytic calculations, that the adaptively-driven dynamical hair cell model violates both the FDT and the GFDT. We go on to show, using stochastic, fini...
Thermodynamics and the quantum speed limit in the non-Markovian regime
Physical Review A, 2021
Quantum speed limit (QSL) for open quantum systems in the non-Markovian regime is analyzed. We provide a lower bound for the time required to transform an initial state to a final state in terms of thermodynamic quantities such as the energy fluctuation, entropy production rate and dynamical activity. Such bound was already analyzed for Markovian evolution satisfying detailed balance condition. Here we generalize this approach to deal with arbitrary evolution governed by time-local generator. Our analysis is illustrated by three paradigmatic examples of qubit evolution: amplitude damping, pure dephasing, and the eternally non-Markovian evolution.
Single-molecule measurement of the effective temperature in non-equilibrium steady states
Nature Physics, 2015
Temperature is a well-defined quantity for systems in equilibrium. For glassy systems, it has been extended to the non-equilibrium regime, showing up as an e ective quantity in a modified version of the fluctuation-dissipation theorem. However, experimental evidence supporting this definition remains scarce. Here, we present the first direct experimental demonstration of the e ective temperature by measuring correlations and responses in single molecules in non-equilibrium steady states generated under external random forces. We combine experiment, analytical theory and simulations for systems with di erent levels of complexity, ranging from a single bead in an optical trap to two-state and multiple-state DNA hairpins. From these data, we extract a unifying picture for the existence of an e ective temperature based on the relative order of various timescales characterizing intrinsic relaxation and external driving. Our study thus introduces driven small systems as a fertile ground to address fundamental concepts in statistical physics, condensed-matter physics and biophysics.
Activity driven transport in harmonic chains
SciPost Physics
The transport properties of an extended system driven by active reservoirs is an issue of paramount importance, which remains virtually unexplored. Here we address this issue, for the first time, in the context of energy transport between two active reservoirs connected by a chain of harmonic oscillators. The couplings to the active reservoirs, which exert correlated stochastic forces on the boundary oscillators, lead to fascinating behavior of the energy current and kinetic temperature profile even for this linear system. We analytically show that the stationary active current (i) changes non-monotonically as the activity of the reservoirs are changed, leading to a negative differential conductivity (NDC), and (ii) exhibits an unexpected direction reversal at some finite value of the activity drive. The origin of this NDC is traced back to the Lorentzian frequency spectrum of the active reservoirs. We provide another physical insight to the NDC using nonequilibrium linear response ...
Dynamical structure factors of dynamical quantum simulators
Proceedings of the National Academy of Sciences, 2020
Significance Quantum simulators promise to offer new insights into strongly correlated matter beyond what is accessible by means of classical computers. We propose dynamical quantum simulators (DQSs) as a method to simulate dynamical structure factors (DSFs) for system sizes considerably larger than what classical simulations can compute and provide complexity-theoretic evidence that they cannot be classically efficiently computed. Based on state-of-the-art experimental setups, we show how results from DQSs can be directly compared to experiments exploring properties of quantum materials. At the same time, we explore long-ranged spin systems: In particular, we show that the DSFs in DQSs can exhibit the signatures of excitation confinement in long-ranged models for which a comprehensive understanding is lacking.
Glassy dynamics due to a trajectory phase transition in dissipative Rydberg gases
Physical Review A, 2018
The physics of highly excited Rydberg atoms is governed by blockade or exclusion interactions that hinder the excitation of atoms in the proximity of a previously excited one. This leads to cooperative effects and a relaxation dynamics displaying space-time heterogeneity similar to what is observed in the relaxation of glass-forming systems. Here we establish theoretically the existence of a glassy dynamical regime in an open Rydberg gas, associated with phase coexistence at a first-order transition in dynamical large deviation functions. This transition occurs between an active phase of low density in which dynamical processes take place on short timescales, and an inactive phase in which excited atoms are dense and the dynamics is highly arrested. We perform a numerically exact study and develop a mean-field approach that allows us to understand the mechanics of this phase transition. We show that radiative decay-which becomes experimentally relevant for long times-moves the system away from dynamical phase coexistence. Nevertheless, the dynamical phase transition persists and causes strong fluctuations in the observed dynamics.
On the Nonequilibrium Entropy of Large and Small Systems
Stochastic Dynamics Out of Equilibrium, 2019
Thermodynamics makes definite predictions about the thermal behavior of macroscopic systems in and out of equilibrium. Statistical mechanics aims to derive this behavior from the dynamics and statistics of the atoms and molecules making up these systems. A key element in this derivation is the large number of microscopic degrees of freedom of macroscopic systems. Therefore, the extension of thermodynamic concepts, such as entropy, to small (nano) systems raises many questions. Here we shall reexamine various definitions of entropy for nonequilibrium systems, large and small. These include thermodynamic (hydrodynamic), Boltzmann, and Gibbs-Shannon entropies. We shall argue that, despite its common use, the last is not an appropriate physical entropy for such systems, either isolated or in contact with thermal reservoirs: physical entropies should depend on the microstate of the system, not on a subjective probability distribution. To square this point of view with experimental results of Bechhoefer we shall argue that the Gibbs-Shannon entropy of a nano particle in a thermal fluid should be interpreted as the Boltzmann entropy of a dilute gas of Brownian particles in the fluid.
Thermodynamic formula for the cumulant generating function of time-averaged current
Physical Review E, 2011
The cumulant generating function of time-averaged current is studied from an operational viewpoint. Specifically, for interacting Brownian particles under non-equilibrium conditions, we show that the first derivative of the cumulant generating function is equal to the expectation value of the current in a modified system with an extra force added, where the modified system is characterized by a variational principle. The formula reminds us of Einstein's fluctuation theory in equilibrium statistical mechanics. Furthermore, since the formula leads to the fluctuation-dissipation relation when the linear response regime is focused on, it is regarded as an extension of the linear response theory to that valid beyond the linear response regime. The formula is also related to previously known theories such as the Donsker-Varadhan theory, the additivity principle, and the least dissipation principle, but it is not derived from them. Examples of its application are presented for a driven Brownian particle on a ring subject to a periodic potential.
Exact Equalities and Thermodynamic Relations for Nonequilibrium Steady States
Journal of Statistical Physics, 2015
We study thermodynamic operations which bring a nonequilibrium steady state (NESS) to another NESS in physical systems under nonequilibrium conditions. We model the system by a suitable Markov jump process, and treat thermodynamic operations as protocols according to which the external agent varies parameters of the Markov process. Then we prove, among other relations, a NESS version of the Jarzynski equality and the extended Clausius relation. The latter can be a starting point of thermodynamics for NESS. We also find that the corresponding nonequilibrium entropy has a microscopic representation in terms of symmetrized Shannon entropy in systems where the microscopic description of states involves "momenta". All the results in the present paper are mathematically rigorous.
Entropy Production of Nanosystems with Time Scale Separation
Physical review letters, 2016
Energy flows in biomolecular motors and machines are vital to their function. Yet experimental observations are often limited to a small subset of variables that participate in energy transport and dissipation. Here we show, through a solvable Langevin model, that the seemingly hidden entropy production is measurable through the violation spectrum of the fluctuation-response relation of a slow observable. For general Markov systems with time scale separation, we prove that the violation spectrum exhibits a characteristic plateau in the intermediate frequency region. Despite its vanishing height, the plateau can account for energy dissipation over a broad time scale. Our findings suggest a general possibility to probe hidden entropy production in nanosystems without direct observation of fast variables.
Spectral fingerprints of nonequilibrium dynamics: The case of a Brownian gyrator
Physical review, 2022
The same system can exhibit a completely different dynamical behavior when it evolves in equilibrium conditions or when it is driven out-of-equilibrium by, e.g., connecting some of its components to heat baths kept at different temperatures. Here we concentrate on an analytically solvable and experimentally-relevant model of such a system-the so-called Brownian gyrator-a twodimensional nanomachine that performs a systematic, on average, rotation around the origin under non-equilibrium conditions, while no net rotation takes place under equilibrium ones. On this example, we discuss a question whether it is possible to distinguish between two types of a behavior judging not upon the statistical properties of the trajectories of components, but rather upon their respective spectral densities. The latter are widely used to characterize diverse dynamical systems and are routinely calculated from the data using standard built-in packages. From such a perspective, we inquire whether the power spectral densities possess some "fingerprint" properties specific to the behavior in non-equilibrium. We show that indeed one can conclusively distinguish between equilibrium and non-equilibrium dynamics by analyzing the cross-correlations between the spectral densities of both components in the short frequency limit, or from the spectral densities of both components evaluated at zero frequency. Our analytical predictions, corroborated by experimental and numerical results, open a new direction for the analysis of a non-equilibrium dynamics.