  An ensemble of classical subsystems interacting with surrounding particles
has been considered. In general case, a phase volume of the subsystems ensemble
was shown to be a function of time. The evolutional equations of the ensemble
are obtained as well as the simplest solution of these equations representing
the quasi-local distribution with the temperature pattern being assigned.
Unlike the Gibbs's distribution, the energy of interaction with surrounding
particles appears in the distribution function, which make possible both
evolution in the equilibrium case and fluctuations in the non-equilibrium one.
The expression for local entropy is obtained. The exact expressions for
changing entropy and quantity of the heat given by the environment have been
obtained. A two-particle distribution function for pair interaction system has
been obtained with the use of local conditional distribution functions. Its
formula is exact disregarding edge conditions.The derivation of hydrodynamic
equations from Boltzmann equation has been analyzed. The hydrodynamic equations
obtained from Boltzmann equation were shown to be equations for ideal liquid.
Reasons for stochastic description in deterministic Hamilton's systems,
conditions of applicability of Poincares recurrence theorem as well as the
problem of irreversibility have been considered.
