Macroscopic Dynamical Fluctuations in Kac Ring Model

We study dynamical fluctuations in the macroscopic paths around most probable path of Kac ring model, which is a simple deterministic and reversible system exhibiting irreversible relaxation. derive form generating function for show that small deviations are described by discrete-time Ornstein–Uhlenbeck process. also argue microscopic reversibility leads to fluctuation relation rate function, prove it based on function.