The Many Faces of Fluctuation-Dissipation Relations Out of Equilibrium

TL;DR

This paper reviews the evolution of Fluctuation-Dissipation Relations (FDR) from classical to modern stochastic thermodynamics, highlighting two main approaches and their applications in various non-equilibrium systems.

Contribution

It provides a comprehensive overview of FDR theories out of equilibrium, emphasizing recent developments and dual approaches related to stationary distributions and transition rates.

Findings

Two complementary approaches to out-of-equilibrium FDR are discussed.

Applications of FDR are explored in spin models, granular media, and active matter.

The review connects FDR theory to causation and inference in complex systems.

Abstract

In this paper, we offer to the reader an essential review of the theory of Fluctuation-Dissipation Relations (FDR), from the first formulations due to Einstein and Onsager, to the recent developments in the framework of stochastic thermodynamics of non-equilibrium system. We focus on two general approaches, somehow complementary, where out-of-equilibrium contributions to the FDR are expressed in terms of different quantities, related either to the stationary distribution or to the transition rates of the system. In particular, we discuss applications of the FDR in the general field of causation and inference, and in the contexts of non-equilibrium systems, such as spin models, granular media and active matter.