The theory of irreversible processes

TLDR

The paper surveys recent developments in the theory of irreversible processes, noting omissions of irreversible thermodynamics and phenomenological theories, which are covered in referenced books. The study focuses on the assumptions underlying irreversible process theories and their physical consequences. The authors review derivations of master equations by Van Hove and Prigogine, Kubo–Tomita linear response theory, ergodic theorems, and recent work on non‑equilibrium open systems, concluding with illustrative applications. The paper finds that ergodic theorems derived from master equations illuminate the emergence of irreversibility, summarizes formal linear response theory, discusses recent non‑equilibrium open‑system work, and presents illustrative applications.

Abstract

A survey is given of the recent developments in the theory of irreversible processes. Particular emphasis is laid on the derivations of master equations by Van Hove and Prigogine and on the linear response theory initiated by Kubo and Tomita. The emphasis in the presentation is on the assumptions underlying these theories and the physical consequences that follow from them. The ergodic theorems that follow from the master equations are discussed and the basic problem of how irreversibility arises is reviewed in the light of these recent developments. Formal linear response theory is summarized and the recent work on non-equilibrium open systems is discussed in some detail. Some special applications that illustrate the general theories are presented at the end of the article. Several topics have been omitted - there is no discussion of irreversible thermodynamics or other phenomenological theories, and the theory of thermodynamic Green's function is mentioned only briefly. Both these topics are dealt with in detail in books which we refer to in the references.