Large rare fluctuations in systems with delayed dissipation

TL;DR

This paper investigates the probability distribution and escape rates in systems with delayed dissipation, deriving explicit corrections for small delays and noise correlation times using a variational approach.

Contribution

It introduces a variational framework to analyze large fluctuations in systems with delayed dissipation, including explicit correction formulas for small delays.

Findings

Most probable paths exhibit time reversal symmetry in thermal equilibrium.

Explicit correction formulas for distribution and escape energy are derived for small delays.

The problem reduces to a variational problem involving acausal equations.

Abstract

We study the probability distribution and the escape rate in systems with delayed dissipation that comes from the coupling to a thermal bath. To logarithmic accuracy in the fluctuation intensity, the problem is reduced to a variational problem. It describes the most probable fluctuational paths, which are given by acausal equations due to the delay. In thermal equilibrium, the most probable path passing through a remote state has time reversal symmetry, even though one cannot uniquely define a path that starts from a state with given system coordinate and momentum. The corrections to the distribution and the escape activation energy for small delay and small noise correlation time are obtained in the explicit form.