Fluctuation-response relations for nonequilibrium diffusions with memory

TL;DR

This paper extends the fluctuation-dissipation theorem to nonequilibrium Langevin systems with memory, revealing how memory effects influence diffusion, mobility, and correlations in complex particle dynamics.

Contribution

It introduces a generalized fluctuation-response relation for nonequilibrium diffusions with memory, expanding the classical understanding to include memory effects and correlations.

Findings

Extended fluctuation-dissipation theorem for systems with memory

Revealed the role of dynamical activity and velocity correlations

Connected nonequilibrium corrections to particle displacement and driving force

Abstract

Strong interaction with other particles or feedback from the medium on a Brownian particle entail memory effects in the effective dynamics. We discuss the extension of the fluctuation-dissipation theorem to nonequilibrium Langevin systems with memory. An important application is to the extension of the Sutherland-Einstein relation between diffusion and mobility. Nonequilibrium corrections include the time-correlation between the dynamical activity and the velocity of the particle, which in turn leads to information about the correlations between the driving force and the particle's displacement.