Martingale properties of entropy production and a generalized work theorem with decoupled forward and backward processes

TL;DR

This paper develops a new framework using martingales and stochastic calculus to generalize work theorems and analyze entropy production in both overdamped and underdamped Langevin systems, including far-from-equilibrium cases.

Contribution

It introduces a novel approach decoupling forward and backward trajectories to derive generalized work theorems with conditioned expectations.

Findings

Constructed martingales for Langevin dynamics

Extended work theorems to arbitrary initial states

Analyzed work theorem violations in far-from-equilibrium systems

Abstract

By decoupling forward and backward stochastic trajectories, we construct a family of martingales and work theorems for both overdamped and underdamped Langevin dynamics. Our results are made possible by an alternative derivation of work theorems that uses tools from stochastic calculus instead of path-integration. We further strengthen the equality in work theorems by evaluating expectations conditioned on an arbitrary initial state value. These generalizations extend the applicability of work theorems and offer new interpretations of entropy production in stochastic systems. Lastly, we discuss the violation of work theorems in far-from-equilibrium systems.