Energy representation for out-of-equilibrium Brownian-like systems: steady states and fluctuation relations

TL;DR

This paper employs energy-based stochastic dynamics to analyze non-equilibrium Brownian-like systems, deriving steady state properties and fluctuation relations like the Jarzynski equality, advancing understanding of out-of-equilibrium thermodynamics.

Contribution

It introduces a Langevin equation with multiplicative noise for energy dynamics and derives generalized fluctuation theorems for non-equilibrium steady states.

Findings

Steady state energy distributions are obtained from the Fokker-Planck equation.

A generalized integral fluctuation theorem is established for systems with shifted probability flux.

Standard fluctuation relations like the Jarzynski equality are derived within this framework.

Abstract

Stochastic dynamics in the energy representation is employed as a method to study non-equilibrium Brownian-like systems. It is shown that the equation of motion for the energy of such systems can be taken in the form of the Langevin equation with multiplicative noise. Properties of the steady states are examined by solving the Fokker-Planck equation for the energy distribution functions. The generalized integral fluctuation theorem is deduced for the systems characterized by the shifted probability flux operator. There are a number of entropy and fluctuation relations such as the Hatano-Sasa identity and the Jarzynski's equality that follow from this theorem.