Fluctuation-dissipation relations: achievements and misunderstandings

TL;DR

This paper reviews the development and understanding of generalized fluctuation-dissipation relations, highlighting their origins, interpretations, and connections to fluctuation theorems, emphasizing historical and conceptual insights.

Contribution

It clarifies the historical development of fluctuation-dissipation relations and their relation to fluctuation theorems, based on the authors' early work from 1977-1984.

Findings

Old results encompass various fluctuation relations

Connections between fluctuation-dissipation relations and fluctuation theorems clarified

Historical perspective on the development of these relations provided

Abstract

We discuss the "generalized fluctuation-dissipation relations (theorems)" for the first time suggested by us in 1977-1984 as statistical-thermodynamical consequences of time symmetry (reversibility) of microscopic dynamics. It is shown, in particular, that our old results in essence contain, as alternative formulations or special cases, various similar relations, including the "fluctuation theorems", what appeared after 1990.