A mathematical description of the evolution of the state of infinite systems of classical statistical mechanics

Abstract

CONTENTS Introduction Chapter I. The Cauchy problem for a chain of Bogolyubov equations § 1. The Bogolyubov equations for symmetric systems § 2. The Bogolyubov equations for symmetric systems of particles with a hard core § 3. The Bogolyubov equations for non-symmetric systems § 4. The formal determination of the evolution operator from the chain of Bogolyubov equations Chapter II. The justification of the solution of the Cauchy problem for the Bogolyubov equations in the space of sequences of summable functions § 1. Symmetric systems § 2. Non-symmetric systems Chapter III. Initial data § 1. Equilibrium distribution functions § 2. Local perturbations of equilibrium distribution functions Chapter IV. The thermodynamic limit in one-dimensional non-equilibrium systems § 1. Solution of the Cauchy problem for the Bogolyubov equations of symmetric systems in the space of sequences of bounded functions § 2. The existence of the thermodynamic limit for symmetric systems § 3. Global solutions § 4. The thermodynamic limit for non-symmetric systems References