Variational Principle in Langevin Processes

TL;DR

This paper generalizes the Nemoto-Sasa variational principle for large deviations in nonequilibrium Langevin processes by revealing a hidden mathematical structure related to the fluctuation-response relation and emphasizing the role of Kullback-Leibler divergence.

Contribution

It introduces a generalized variational framework for Langevin processes, connecting large deviations to fluctuation-response relations through a new mathematical structure.

Findings

Revealed a hidden structure in fluctuation-response relations.

Extended the variational principle to more general Langevin systems.

Highlighted the importance of Kullback-Leibler divergence in the analysis.

Abstract

The recent work, Nemoto and Sasa [Phys. Rev. E, 83: 030105(R) (2011)], has shown that large deviations of the current characterizing a nonequilibrium system are obtained by observing the typical current for a modified system specified by a variational principle. In the present study, we will give a generalized version of the Nemoto-Sasa study by extracting a hidden mathematical structure from the fluctuation-response relation which is well-known in statistical mechanics. Here, the minimization of the Kullback-Leibler divergence plays an essential role.