  The structure of very complicated irregular "microscopic" (local) entropy
fluctuations around a big separated "macroscopic" (global) fluctuation in the
statistical equilibrium was studied in numerical experiments on a simple
2--freedom strongly chaotic Hamiltonian model described by the modified Arnold
cat map. A comparison of transient nonequilibrium rise and relaxation process
of the big fluctuation out of the statistical equilibrium with a nonequilibrium
steady state in a model without statistical equilibrium is considered and
discussed with respect to the so-called Fluctuation Law (or "theorem")
introduced and intensively studied recently in the latter case. A new transient
fluctuation law was found on the basis of a simple semiempirical theory
developed. Preliminary results of numerical experiments on some fractal
properties of the "microscopic" fluctuations are presented and briefly
discussed.
