Symmetries and Geometrical Properties of Dynamical Fluctuations in Molecular Dynamics

Robert Jack,Marcus Kaiser,Johannes Zimmer

doi:10.3390/e19100562

Robert Jack, Marcus Kaiser + Show 1 more

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https://doi.org/10.3390/e19100562

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Journal: Entropy	Publication Date: Oct 22, 2017
Citations: 4	License type: CC BY 4.0

Affiliation: University of Cambridge, University of Bath

Abstract

We describe some general results that constrain the dynamical fluctuations that can occur in non-equilibrium steady states, with a focus on molecular dynamics. That is, we consider Hamiltonian systems, coupled to external heat baths, and driven out of equilibrium by non-conservative forces. We focus on the probabilities of rare events (large deviations). First, we discuss a PT (parity-time) symmetry that appears in ensembles of trajectories where a current is constrained to have a large (non-typical) value. We analyse the heat flow in such ensembles, and compare it with non-equilibrium steady states. Second, we consider pathwise large deviations that are defined by considering many copies of a system. We show how the probability currents in such systems can be decomposed into orthogonal contributions that are related to convergence to equilibrium and to dissipation. We discuss the implications of these results for modelling non-equilibrium steady states.

Highlights

This article studies dynamical fluctuations in stochastic processes of relevance for molecular dynamics
We focus on large deviation principles, which encode the probability of rare dynamical events [1] and discuss the physical principles and symmetries that govern the probabilities of such events
This coupling is especially important if we aim to describe non-equilibrium steady states, in which the work done by external forces must be dissipated in the environment

Summary

Introduction

This article studies dynamical fluctuations in stochastic processes of relevance for molecular dynamics. We consider stochastic systems described by underdamped Langevin equations. We focus on large deviation principles, which encode the probability of rare dynamical events [1] and discuss the physical principles and symmetries that govern the probabilities of such events. The applications we have in mind are physical systems of interacting atoms and molecules, which are usually thought of as evolving by deterministic (Hamiltonian) dynamics. It is standard to add stochastic terms to these equations of motion to describe the coupling of these systems to their environments. This coupling is especially important if we aim to describe non-equilibrium steady states, in which the work done by external forces must be dissipated in the environment

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