On the energy-probability interconnection in the models of classical statistical physics

A new point of view on the mathematical foundations of statistical physics is presented. The concept of the transition energy function of a physical system from one state to another is introduced as the basic one. This function, in contrast to Hamiltonian, has a clear physical meaning and is described by the natural, physically justified properties that transition energy should possess. The reasoning used in the proposed theory is directly related to the solution of Dobrushin's problem of description of specification in terms of one-point distributions parameterized by infinite boundary conditions. Our approach made it possible to give a rigorous mathematical justification for the Gibbs formula, which connects the potential energy of a state of a physical system with the probability of finding it in this state.