Nonrecurrence problem in evolution of a hard-disk system

The evolution of a hard-disk system has been investigated on the bases of the matrix of pair collision (MPC). With the help of MPC the motion equations of this system have been derived. From the properties of the motion equations it was found that as a result of collisions the integral force acting on any disk subsystem tends to zero. It was found that the magnitude of possible fluctuations in the system is to be defined by the condition t(fluct) less than or equal to t(kin), where t(kin) is the characteristic time, which determined by kinetic potential defined relevant point of a phase space. The t(fluct) time is determined by the probability laws. The analysis of the obtained results testifies that the nature of the nonrecurrence are determined by the fundamental symmetry principles.