Unified formalism for entropy productions and fluctuation relations

Abstract

Stochastic entropy production, which quantifies the difference between the probabilities of trajectories of a stochastic dynamics and its time reversals, has a central role in nonequilibrium thermodynamics. In the theory of probability, the change in the statistical properties of observables can be represented by a change in the probability measure. We consider operators on the space of probability measure that induce changes in the statistical properties of a process, and formulate entropy productions in terms of these change-of-probability-measure (CPM) operators. This mathematical underpinning of the origin of entropy productions allows us to achieve an organization of various forms of fluctuation relations: All entropy productions have a non-negative mean value, admit the integral fluctuation theorem, and satisfy a rather general fluctuation relation. Other results such as the transient fluctuation theorem and detailed fluctuation theorems then are derived from the general fluctuation relation with more constraints on the operator. We use a discrete-time, discrete-state-space Markov process to draw the contradistinction among three reversals of a process: time reversal, protocol reversal and the dual process. The properties of their corresponding CPM operators are examined, and the domains of validity of various fluctuation relations for entropy productions in physics and chemistry are revealed. We also show that our CPM operator formalism can help us rather easily extend other fluctuations relations for excess work and heat, discuss the martingale properties of entropy productions, and derive the stochastic integral formulas for entropy productions in constant-noise diffusion process with Girsanov theorem. Our formalism provides a general and concise way to study the properties of entropy-related quantities in stochastic thermodynamics and information theory.

References in corpus (33)

• A nonequilibrium equality for free energy differences
• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
• Entropy production along a stochastic trajectory and an integral fluctuation theorem
• A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
• Fluctuation theorem for stochastic dynamics
• Path ensembles averages in systems driven far-from-equilibrium
• Dynamical ensembles in stationary states
• Steady State Thermodynamics of Langevin Systems
• Three detailed fluctuation theorems
• Fluctuation theorems for stochastic dynamics
• The thermodynamics of prediction
• The Physical Origins of Entropy Production, Free Energy Dissipation and their Mathematical Representations
• Path-integral analysis of fluctuation theorems for general Langevin processes
• Relative Entropy: Free Energy Associated with Equilibrium Fluctuations and Nonequilibrium Deviations
• Mesoscopic Nonequilibrium Thermodynamics of Single Macromolecules and Dynamic Entropy-Energy Compensation
• Experimental test of the differential fluctuation theorem and a generalized Jarzynski equality for arbitrary initial states
• The Fluctuation Theorem for Stochastic Systems
• Statistics of Infima and Stopping Times of Entropy Production and Applications to Active Molecular Processes
• Non-equilibrium thermodynamics of stochastic systems with odd and even variables
• Two refreshing views of Fluctuation Theorems through Kinematics Elements and Exponential Martingale
• Pathwise Construction of Stochastic Integrals
• Joint probability distributions and fluctuation theorems
• Detailed Fluctuation Theorems: A Unifying Perspective
• Time reversibility and nonequilibrium thermodynamics of second-order stochastic processes
• Martingale theory for housekeeping heat
• The Zeroth Law of Thermodynamics and Volume-Preserving Conservative Dynamics with Equilibrium Stochastic Damping
• Fluctuations When Driving Between Nonequilibrium Steady States
• Nonequilibrium thermodynamics and information theory: Basic concepts and relaxing dynamics
• Stochastic thermodynamics with odd controlling parameters
• The Measure-theoretic Identity Underlying Transient Fluctuation Theorems
• Nonlinear Stochastic Dynamics of Complex Systems, II: Potential of Entropic Force in Markov Systems with Nonequilibrium Steady State, Generalized Gibbs Function and Criticality
• Stochastic Dynamics II: Finite Random Dynamical Systems, Linear Representation, and Entropy Production

Cited by in corpus (17)

• Improved bounds on entropy production in living systems
• Thermodynamics of Gambling Demons
• Universal tradeoff relation between speed, uncertainty, and dissipation in nonequilibrium stationary states
• Stochastic thermodynamics of relativistic Brownian motion
• Nonequilibrium thermodynamics of the asymmetric Sherrington-Kirkpatrick model
• Extreme value statistics of edge currents in Markov jump processes and their use for entropy production estimation
• Bivectorial Nonequilibrium Thermodynamics: Cycle Affinity, Vorticity Potential, and Onsager's Principle
• Revisit of macroscopic dynamics for some non-equilibrium chemical reactions from a Hamiltonian viewpoint
• Potentials of Continuous Markov Process and Random Perturbations
• Hierarchical structure of fluctuation theorems for a driven system in contact with multiple heat reservoirs
• Representations and Divergences in the Space of Probability Measures and Stochastic Thermodynamics
• First and Second Laws of Information Processing by Nonequilibrium Dynamical States
• State-space kinetic Ising model reveals task-dependent entropy flow in sparsely active nonequilibrium neuronal dynamics
• Thermodynamic bounds and symmetries in first-passage problems of fluctuating currents
• Jarzyski's equality and Crooks' fluctuation theorem for general Markov chains with application to decision-making systems
• Stochastic Thermodynamics of Non-reciprocally Interacting Particles and Fields
• Nonequilibrium Stationary Process and Fluctuation-Dissipation Relations