Symmetries and Geometrical Properties of Dynamical Fluctuations in Molecular Dynamics

TL;DR

This paper investigates the symmetries and geometrical features of rare dynamical fluctuations in non-equilibrium molecular dynamics, revealing PT symmetry and decomposing probability currents to understand steady state behaviors.

Contribution

It introduces a PT symmetry in trajectory ensembles and a decomposition of probability currents, advancing understanding of non-equilibrium fluctuations in molecular systems.

Findings

PT symmetry constrains large deviation probabilities

Probability currents decompose into orthogonal components

Results inform modeling of non-equilibrium steady states

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.