Fluctuation-dissipation relations: achievements and misunderstandings

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.

💡 Research Summary

The paper revisits the “generalized fluctuation‑dissipation relations” (FDR) originally introduced by the authors between 1977 and 1984, and places them in the context of the later‑emerging fluctuation theorems, especially the Jarzynski equality (JE) and Crooks relation (CR). The authors argue that their earlier results already contain, as special cases or alternative formulations, many of the relations that have been rediscovered under the banner of fluctuation theorems after 1997.

The introduction emphasizes a crucial distinction between closed systems—those that possess a well‑defined thermodynamic equilibrium for any value of an external parameter x—and open systems, which lack an equilibrium when x≠0 (for example, a rotator driven by a constant torque). In closed systems the free energy F(x) is defined for all x, and JE/CR connect work fluctuations to the free‑energy difference ΔF. In open systems, however, F(x) does not exist, so ΔF is meaningless and JE/CR cannot be applied directly.

The authors then present the Bochkov‑Kuzovlev equality (BKE), derived from microscopic time‑reversal symmetry and the Liouville theorem. The central identity is

  P(Π⁺) exp