Nonequilibrium Stationary Process and Fluctuation-Dissipation Relations

Abstract

A stochastic dynamics has a natural decomposition into a drift capturing mean rate of change and a martingale increment capturing randomness. They are two statistically uncorrelated, but not necessarily independent mechanisms contributing to the overall fluctuations of the dynamics, representing the uncertainties in the past and in the future. A generalized Einstein relation is a consequence solely because the dynamics being stationary; and the Green-Kubo formula reflects a balance between the two mechanisms. Equilibrium with reversibility is characterized by a novel covariance symmetry.

References in corpus (10)

• Thermodynamic uncertainty relation for biomolecular processes
• Stochastic Dynamical Structure (SDS) of Nonequilibrium Processes in the Absence of Detailed Balance. II: construction of SDS with nonlinear force and multiplicative noise
• Generic Properties of Stochastic Entropy Production
• Entropic bounds on currents in Langevin systems
• On the Application of the Gallavotti-Cohen Fluctuation Relation to Thermostatted Steady States Near Equilibrium
• Thermodynamics of Gambling Demons
• Fluctuation-dissipation relations far from equilibrium
• Mathematical Formalism for Isothermal Linear Irreversibility
• Unified formalism for entropy productions and fluctuation relations
• Martingale theory for housekeeping heat