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