On the fluctuation-dissipation relation in non-equilibrium and non-Hamiltonian systems.

Area of Science:

• Statistical Mechanics
• Non-equilibrium Physics
• Complex Systems

Background:

• Standard fluctuation-dissipation relations apply to systems in equilibrium.
• Nonstandard systems, such as those out of equilibrium or lacking Hamiltonian structure, require generalized approaches.
• Understanding system dynamics and responses is crucial in diverse physical contexts.

Purpose of the Study:

• To review generalized fluctuation-dissipation relations applicable to nonstandard systems.
• To demonstrate how response functions can be derived from correlation functions in unperturbed dynamics.
• To highlight the role of stationary probability distributions in capturing system interactions.

Main Methods:

• Review of theoretical frameworks for generalized fluctuation-dissipation relations.
• Expression of response functions using correlation functions from unperturbed dynamics.
• Analysis of contributions from stationary probability distributions.

Main Results:

• Generalized fluctuation-dissipation relations are valid for systems out of equilibrium and without Hamiltonian structure.
• Response functions are expressible via correlation functions of the unperturbed dynamics.
• Stationary probability distributions yield nontrivial contributions, reflecting inter-degree-of-freedom interactions.

Conclusions:

• The reviewed formalism provides a unified approach for analyzing diverse nonstandard systems.
• Generalized fluctuation-dissipation relations are powerful tools for studying complex systems.
• Applications include driven granular media, multiscale systems, active matter, and anomalous diffusion.