Kinetic equation for a system of many strongly interacting particles and the law of increasing entropy

Using the Bogoliubov method [1], the kinetic equation for density matrix of macroscopic subsystem is obtained, which represents a generalisation of the Boltzmann equation to the case of a system of particles with strong interaction. It is shown that the solutions of this equation are in accordance with the law of increasing entropy and describe the relaxation of the system to the equilibrium Gibbs distribution. The solution of the problem, how make the irreversible character of the kinetic equation to be compatible with the reversibility of the equations of mechanics, is given, and the necessary and sufficient conditions of the existence of kinetic equations are formulated.