Mathematical Formalism for Isothermal Linear Irreversibility

Abstract

We prove the equivalence among symmetricity, time reversibility, and zero entropy production of the stationary solutions of linear stochastic differential equations. A sufficient and necessary reversibility condition expressed in terms of the coefficients of the equations is given. The existence of a linear stationary irreversible process is established. Concerning reversibility, we show that there is a contradistinction between any 1-dimensional stationary Gaussian process and stationary Gaussian process of dimension $n>1$. A concrete criterion for differentiating stationarity and sweeping behavior is also obtained. The mathematical result is a natural generalization of Einstein's fluctuation-dissipation relation, and provides a rigorous basis for the isothermal irreversibility in a linear regime which is the basis for applying Onsager's theory to macromolecules in aqueous solution.

15 pages

References in corpus (3)

• A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
• Relative Entropy: Free Energy Associated with Equilibrium Fluctuations and Nonequilibrium Deviations
• The Mathematical Theory of Molecular Motor Movement and Chemomechanical Energy Transduction

Cited by in corpus (23)

• Structure of Stochastic Dynamics near Fixed Points
• Mesoscopic Nonequilibrium Thermodynamics of Single Macromolecules and Dynamic Entropy-Energy Compensation
• The Mathematical Theory of Molecular Motor Movement and Chemomechanical Energy Transduction
• Thermodynamic Limit of a Nonequilibrium Steady-State: Maxwell-Type Construction for a Bistable Biochemical System
• Entropy production of Multivariate Ornstein-Uhlenbeck processes correlates with consciousness levels in the human brain
• A Decomposition of Irreversible Diffusion Processes Without Detailed Balance
• Statistical Thermodynamics of General Minimal Diffusion Processes: Constuction, Invariant Density, Reversibility and Entropy Production
• Equations for Stochastic Macromolecular Mechanics of Single Proteins: Equilibrium Fluctuations, Transient Kinetics and Nonequilibrium Steady-State
• Characterising the nonequilibrium stationary states of Ornstein-Uhlenbeck processes
• Thermodynamics of the General Diffusion Process: Equilibrium Supercurrent and Nonequilibrium Driven Circulation with Dissipation
• Dynamic Looping of a Free-Draining Polymer
• Asymptotics of Sample Entropy Production Rate for Stochastic Differential Equations
• Stochastic limit-cycle oscillations of a nonlinear system under random perturbations
• Circular Stochastic Fluctuations in SIS Epidemics with Heterogeneous Contacts Among Sub-populations
• The Large Deviation Principle and Steady-state Fluctuation Theorem for the Entropy Production Rate of a Stochastic Process in Magnetic Fields
• The Fluctuation-Dissipation Relations: Growth, Diffusion, and Beyond
• Asymptotics of the entropy production rate for $d$-dimensional Ornstein-Uhlenbeck processes
• Large Deviations of the Entropy Production Rate for a Class of Gaussian Processes
• One-Dimensional Birth-Death Process and Delbrück-Gillespie Theory of Mesoscopic Nonlinear Chemical Reactions
• Universal Ideal Behavior and Macroscopic Work Relation of Linear Irreversible Stochastic Thermodynamics
• Nonequilibrium Stationary Process and Fluctuation-Dissipation Relations
• Stochastic entropy production in diffusive systems
• Mesoscopic and Macroscopic Entropy Balance Equations in a Stochastic Dynamics and Its Deterministic Limit