An expression for stationary distribution in nonequilibrium steady state

Abstract

We study the nonequilibrium steady state realized in a general stochastic system attached to multiple heat baths and/or driven by an external force. Starting from the detailed fluctuation theorem we derive concise and suggestive expressions for the corresponding stationary distribution which are correct up to the second order in thermodynamic forces. The probability of a microstate $\eta$ is proportional to $\exp [\Phi (\eta )]$ where $\Phi (\eta )=-{\sum }_k{\beta }_k{\mathcal{E}}_k(\eta )$ is the excess entropy change. Here ${\mathcal{E}}_k(\eta )$ is the difference between two kinds of conditioned path ensemble averages of excess heat transfer from the $k$-th heat bath whose inverse temperature is ${\beta }_k$. Our expression may be verified experimentally in nonequilibrium states realized, for example, in mesoscopic systems.

4 pages, 2 figures

References in corpus (8)

• Dynamical Ensembles in Nonequilibrium Statistical Mechanics
• Fluctuation theorem for stochastic dynamics
• Opportunities for mesoscopics in thermometry and refrigeration: Physics and applications
• Path ensembles averages in systems driven far-from-equilibrium
• Steady State Thermodynamics of Langevin Systems
• The Fluctuation Theorem as a Gibbs Property
• Linear response theory in stochastic many-body systems revisited
• Hidden heat transfer in equilibrium states implies directed motion in nonequilibrium states

Cited by in corpus (60)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Nonequilibrium Thermodynamics of Feedback Control
• Frenesy: time-symmetric dynamical activity in nonequilibria
• Steady State Thermodynamics for Heat Conduction -- Microscopic Derivation
• Active Brownian Heat Engines
• Geometrical Expression of Excess Entropy Production
• A nonequilibrium extension of the Clausius heat theorem
• Response theory: a trajectory-based approach
• Thermodynamic formula for the cumulant generating function of time-averaged current
• A meaningful expansion around detailed balance
• Heat capacity in nonequilibrium steady states
• How dissipation constrains fluctuations in nonequilibrium liquids: Diffusion, structure and biased interactions
• Representation of nonequilibrium steady states in large mechanical systems
• Rigorous meaning of McLennan ensembles
• Stochastic thermodynamics for delayed Langevin systems
• Non-equilibrium fluctuations for linear diffusion dynamics
• Quantum thermalization of two coupled two-level systems in eigenstate and bare-state representations
• Limits of Predictions in Thermodynamic Systems: A Review
• Revisiting the Glansdorff-Prigogine criterion for stability within irreversible thermodynamics
• Nonequilibrium Steady State Driven by a Nonlinear Drift Force
• Thermal ratchet effect in confining geometries
• Liquid-gas transitions in steady heat conduction
• Emergent second law for non-equilibrium steady states
• Transport coefficients for a confined Brownian ratchet operating between two heat reservoirs
• Exact equalities and thermodynamic relations for nonequilibrium steady states
• Global Thermodynamics for Heat Conduction Systems
• Trees and forests for nonequilibrium purposes: an introduction to graphical representations
• Nonequilibrium mode-coupling theory for uniformly sheared underdamped systems
• Macroscopic Expression Connecting the Rate of Energy Dissipation and Violation of the Fluctuation-Response Relation
• Work Relation and the Second Law of Thermodynamics in Nonequilibrium Steady States
• Statistical forces from close--to--equilibrium media
• Zeroth law of thermodynamics for nonequilibrium steady states in contact
• Theoretical approaches to the steady-state statistical physics of interacting dissipative units
• Large deviations and chemical potential in bulk-driven systems in contact
• Unique extension of the maximum entropy principle to phase coexistence in heat conduction
• Linear response in large deviations theory: A method to compute non-equilibrium distributions
• Posterior probability and fluctuation theorem in stochastic processes
• Stochastic order parameter dynamics for phase coexistence in heat conduction
• Quantum thermodynamics of nanoscale steady states far from equilibrium
• Nonequilibrium corrections to gradient flow
• Noncyclic and nonadiabatic geometric phase for counting statistics
• Quantitative analysis of Clausius inequality
• A mass transport model with a simple non-factorized steady-state distribution
• Universal expression for adiabatic pumping in terms of non-equilibrium steady states
• Active Fluctuation Symmetries
• Thermodynamics of nonequilibrium driven diffusive systems in mild contact with boundary reservoirs
• Nonequilibrium steady state of the kinetic Glauber-Ising model under an alternating magnetic field
• Entropy-based characterizations of the observable-dependence of the fluctuation-dissipation temperature
• Free energy for non-equilibrium quasi-stationary states
• Nonequilibrium chemical potentials of steady-state lattice gas models in contact: A large-deviations approach
• Long-range correlations in a simple stochastic model of coupled transport
• Close-to-equilibrium heat capacity
• Work relations for time-dependent states
• Contact geometry and quantum thermodynamics of nanoscale steady states
• The McLennan-Zubarev steady state distribution and fluctuation theorems
• Steady-state thermodynamics for population dynamics in fluctuating environments with side information
• Reformulating non-equilibrium steady-states and generalised Hopfield discrimination
• Thermodynamics of stationary states of the ideal gas in a heat flow
• Noncyclic geometric phase in counting statistics and its role as an excess contribution
• The Steady State Distribution of the Master Equation