Nonequilibrium Stationary Process and Fluctuation-Dissipation Relations

TL;DR

This paper explores the decomposition of stochastic dynamics into drift and martingale components, revealing how fluctuation-dissipation relations emerge from stationarity and introducing a new covariance symmetry for equilibrium.

Contribution

It provides a theoretical framework linking stationary stochastic processes with generalized fluctuation-dissipation relations and introduces a novel covariance symmetry for reversible equilibrium.

Findings

Generalized Einstein relation arises from stationarity

Green-Kubo formula reflects balance between mechanisms

Reversibility characterized by covariance symmetry

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.