Functional Approach to Classical Non-Equilibrium Statistical Mechanics

Abstract

A new approach to classical non‐equilibrium statistical mechanics is considered. The essential idea is to solve Bogoliubov's functional‐differential equation for the generating functional embracing all distribution functions for the particle system with the aid of the technique of functional integration. It becomes possible with a minor modification of his formalism. A general solution is given. The solution for our state functional is reduced to the Hopf characteristic functional for the Vlasov selfconsistent field when the interaction energy of particles is relatively small in each s‐body Hamiltonian H_s.