Stochastic theory of the classical molecular dynamics method

The work is devoted to the fundamental aspects of the classical molecular dynamics method, which originated half a century ago as a method of solving computational problems in statistical physics and has become by now one of the most important numerical methods in the theory of condensed matter. However, the molecular dynamics method based on solving the equations of motion for many-particle system, was directly related to the basic concepts of classical statistical physics, in particular, the problem of irreversibility. This paper analyzes the dynamic and stochastic properties of the molecular-dynamical systems related to the local instability of trajectories and the errors of numerical integration. The probabilistic nature of classical statistics is discussed. The finite vlues of the dynamic memory time and the emergence of irreversibility in real systems are explained.