Fluctuation-Dissipation: Response Theory in Statistical Physics

TL;DR

This paper reviews the Fluctuation-Dissipation Relation and Response Theory, highlighting their historical development, general applicability beyond Hamiltonian systems, and recent advances connecting them to Fluctuation Relations in non-equilibrium systems.

Contribution

It provides a comprehensive overview of the FDR's conceptual foundations, its generalization beyond Hamiltonian systems, and recent developments linking it to Fluctuation Relations and large deviation theory.

Findings

FDR applies broadly beyond Hamiltonian systems.

Recent work connects FDR with Fluctuation Relations in non-equilibrium.

Examples include fluids, granular media, nano-systems, and biological systems.

Abstract

General aspects of the Fluctuation-Dissipation Relation (FDR), and Response Theory are considered. After analyzing the conceptual and historical relevance of fluctuations in statistical mechanics, we illustrate the relation between the relaxation of spontaneous fluctuations, and the response to an external perturbation. These studies date back to Einstein's work on Brownian Motion, were continued by Nyquist and Onsager and culminated in Kubo's linear response theory. The FDR has been originally developed in the framework of statistical mechanics of Hamiltonian systems, nevertheless a generalized FDR holds under rather general hypotheses, regardless of the Hamiltonian, or equilibrium nature of the system. In the last decade, this subject was revived by the works on Fluctuation Relations (FR) concerning far from equilibrium systems. The connection of these works with large deviation theory is analyzed. Some examples, beyond the standard applications of statistical mechanics, where fluctuations play a major role are discussed: fluids, granular media, nano-systems and biological systems.