Non-Markovian Model for the Approach to Equilibrium

This paper is intended to provide the axiomatic study of nonequilibrium quantum statistical mechanics with some simple and rigorously solvable models. The models considered here are obtained as generalizations of the Ising model. They illustrate and allow a rational discussion of the following concepts relevant to the theory of irreversible phenomena: coarse-graining and time-smoothing, ergodicity, recurrences, impossibility of a Markovian description of the approach to equilibrium for some physical systems, justification of the various random phase assumptions, properties of the interaction responsible for the approach to equilibrium, master equations, etc.