Irreversible Boltzmann samplers in dense liquids: weak-coupling approximation and mode-coupling theory

TL;DR

This paper investigates how transverse forces can accelerate the dynamics of dense liquids out of equilibrium, developing a mode-coupling theory and confirming results with numerical data, especially near the glass transition.

Contribution

It introduces a nonequilibrium mode-coupling theory to quantify the acceleration effects of transverse forces in dense liquids, extending understanding of nonequilibrium dynamics.

Findings

Transverse forces increase mobility and diffusivity.

Acceleration decreases as temperature approaches the glass transition.

Theoretical predictions agree with numerical simulations.

Abstract

Exerting a nonequilibrium drive on an otherwise equilibrium Langevin process brings the dynamics out of equilibrium but can also speedup the approach to the Boltzmann steady-state. Transverse forces are a minimal framework to achieve dynamical acceleration of the Boltzmann sampling. We consider a simple liquid in three space dimensions subjected to additional transverse pairwise forces, and quantify the extent to which transverse forces accelerate the dynamics. We first explore the dynamics of a tracer in a weak coupling regime describing high temperatures. The resulting acceleration is correlated with a monotonous increase of the magnitude of odd transport coefficients (mobility and diffusivity) with the amplitude of the transverse drive. We then develop a nonequilibrium version of the mode-coupling theory able to capture the effect of transverse forces, and more generally of forces created by additional degrees of freedom. Based on an analysis of transport coefficients, both odd and longitudinal, both for the collective modes and for a tracer particle, we find a systematic acceleration of the dynamics. Quantitatively, the gain, which is guaranteed throughout the ergodic phase, turns out to be a decreasing function of temperature beyond a temperature crossover, in particular as the glass transition is approached. Our theoretical results are in good agreement with available numerical results.