Free energy dissipation and a decomposition of general jump diffusions on $\mathbb{R}^n$ without detailed balance

TL;DR

This paper explores the thermodynamic structure of jump diffusions combining Brownian and Poisson noise, revealing a decomposition of free energy dissipation into entropy production and housekeeping heat, with implications for nonequilibrium statistical physics.

Contribution

It introduces a novel decomposition of the generator into symmetric and anti-symmetric parts for jump diffusions, clarifying the structure of nonequilibrium stationary states.

Findings

Free energy dissipation decomposes into entropy production and housekeeping heat.

Symmetric sector relates to reversible dynamics and Fisher information.

Anti-symmetric sector generates circulation without dissipation.

Abstract

We analyze the thermodynamic structure of jump diffusions combining Brownian and Poisson noise, a class of stochastic dynamics relevant to nonequilibrium statistical physics. For such nonlocal dynamics, the free energy admits a full dissipation formula that decomposes into entropy production and housekeeping heat. A central result is a decomposition of the generator into symmetric and anti-symmetric parts with respect to the invariant measure $\rho_{ss}$. The symmetric sector corresponds to a reversible dynamics and yields a nonlocal Fisher information governing free-energy decay, whereas the anti-symmetric sector generates a canonical conservative flow that produces circulation but no dissipation. Several numerical examples demonstrate how this decomposition clarifies the structure of nonequilibrium stationary states in jump-driven systems.