Entropy production rate and time-reversibility for general jump diffusions on $\mathbb{R}^n$

TL;DR

This paper studies the entropy production rate and time-reversibility in general jump diffusions, establishing key thermodynamic relations and conditions for reversibility based on relative entropy and the Girsanov transform.

Contribution

It introduces a formulation of entropy production rate for jump diffusions and links it to time-reversibility, detailed balance, and gradient structures in a unified framework.

Findings

Derived the entropy production rate using relative entropy and Girsanov transform.

Established the equivalence among time-reversibility, zero entropy production, and detailed balance.

Provided thermodynamic relations for jump diffusions.

Abstract

This paper investigates the entropy production rate and time-reversibility for general jump diffusions (L\'{e}vy processes) on $\mathbb{R}^n$. We first formulate the entropy production rate and explore its associated thermodynamic relations for jump diffusions. Subsequently, we derive the entropy production rate using the relative entropy between the forward and time-reversed path measures for stationary jump diffusions via the Girsanov transform. Furthermore, we establish the equivalence among time-reversibility, zero entropy production rate, detailed balance condition, and the gradient structure for stationary jump diffusions.