On the Fluctuation-Dissipation Relation in non-equilibrium and non-Hamiltonian systems

TL;DR

This paper reviews generalized Fluctuation-Dissipation Relations applicable to non-equilibrium and non-Hamiltonian systems, highlighting their formalism, contributions, and applications to complex systems like active matter and granular media.

Contribution

It introduces a unified formalism for Fluctuation-Dissipation Relations in non-standard systems, including non-equilibrium and non-Hamiltonian cases, with illustrative examples.

Findings

Response functions expressed via correlation functions in unperturbed dynamics

Nontrivial contributions from stationary probability distributions

Applications to driven granular media, active matter, and anomalous diffusion

Abstract

We review generalized Fluctuation-Dissipation Relations which are valid under general conditions even in ``non-standard systems'', e.g. out of equilibrium and/or without a Hamiltonian structure. The response functions can be expressed in terms of suitable correlation functions computed in the unperperturbed dynamics. In these relations, typically one has nontrivial contributions due to the form of the stationary probability distribution; such terms take into account the interaction among the relevant degrees of freedom in the system. We illustrate the general formalism with some examples in non-standard cases, including driven granular media, systems with a multiscale structure, active matter and systems showing anomalous diffusion.