Dissipating the Langevin equation in the presence of an external stochastic potential

TL;DR

This paper investigates methods to dissipate the Langevin equation with a space-dependent stochastic potential, comparing a mean-field friction approach with a local friction approach, and evaluates their effectiveness in maintaining temperature and equipartition.

Contribution

It evaluates the effectiveness of space-dependent friction in Langevin dynamics with stochastic potentials, highlighting limitations due to neglecting memory effects.

Findings

Space-dependent friction can maintain temperature similar to mean-field methods.

Deviations from equipartition occur when memory effects are ignored.

The approach works well in simple one-dimensional stochastic potentials.

Abstract

In the Langevin formalism, the delicate balance maintained between the fluctuations in the system and their corresponding dissipation may be upset by the presence of a secondary, space-dependent stochastic force, particularly in the low friction regime. In prior work, the latter was dissipated self-consistently through an additional uniform (mean-field) friction [Shepherd and Hernandez, J. Chem. Phys., 115, 2430-2438 (2001).] An alternative approach to ensure that equipartition is satisfied relies on the use of a space-dependent friction while ignoring nonlocal correlations. The approach is evaluated with respect to its ability to maintain constant temperature for two simple one-dimensional, stochastic potentials of mean force wherein the friction can be evaluated explicitly when there is no memory in the barriers. The use of a space-dependent friction is capable of providing qualitatively similar results to those obtained previously, but in extreme cases, deviations from equipartition may be observed due to the neglect of the memory effects present in the stochastic potentials.