Asymptotics of the Entropy Production Rate for d-Dimensional Ornstein–Uhlenbeck Processes

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 Poincaré inequality and log-Sobolev inequality. As an application, we obtain a law of iterated logarithm for the entropy production rate.