Asymptotics of the entropy production rate for $d$-dimensional Ornstein-Uhlenbeck processes

TL;DR

This paper establishes central limit theorems, moderate deviation principles, and a law of iterated logarithm for the entropy production rate of multi-dimensional Ornstein-Uhlenbeck processes, advancing understanding in non-equilibrium statistical physics.

Contribution

It introduces new probabilistic limit results for entropy production in Ornstein-Uhlenbeck processes using functional inequalities.

Findings

Central limit theorem for entropy production rate

Moderate deviation principle established

Law of iterated logarithm derived

Abstract

In the context of non-equilibrium statistical physics, the entropy production rate is an important concept to describe how far a specific state of a system is from its equilibrium state. In this paper, we establish a central limit theorem and a moderate deviation principle for the entropy production rate of $d$-dimensional Ornstein-Uhlenbeck processes, by the techniques of functional inequalities such as Poincar\'e inequality and log-Sobolev inequality. As an application, we obtain a law of iterated logarithm for the entropy production rate.