Irreversible effects of memory

TL;DR

This paper investigates how memory effects in Langevin dynamics lead to irreversibility and entropy production, especially when the fluctuation-dissipation theorem is violated, and verifies fluctuation relations through simulations.

Contribution

It introduces the concept of 'memory forces' contributing to entropy production and demonstrates their role in irreversibility in systems with memory effects.

Findings

Memory forces contribute to entropy production.

Fluctuation relations are validated when including memory forces.

Inertia and overdamped dynamics yield similar results.

Abstract

The steady state of a Langevin equation with short ranged memory and coloured noise is analyzed. When the fluctuation-dissipation theorem of second kind is not satisfied, the dynamics is irreversible, i.e. detailed balance is violated. We show that the entropy production rate for this system should include the power injected by ``memory forces''. With this additional contribution, the Fluctuation Relation is fairly verified in simulations. Both dynamics with inertia and overdamped dynamics yield the same expression for this additional power. The role of ``memory forces'' within the fluctuation-dissipation relation of first kind is also discussed.