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Entropy 2017, 19(10), 562; https://doi.org/10.3390/e19100562

Symmetries and Geometrical Properties of Dynamical Fluctuations in Molecular Dynamics

1
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
2
Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK
3
Department of Physics, University of Bath, Bath BA2 7AY, UK
4
Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK
*
Author to whom correspondence should be addressed.
Received: 9 September 2017 / Revised: 18 October 2017 / Accepted: 19 October 2017 / Published: 22 October 2017
(This article belongs to the Special Issue Understanding Molecular Dynamics via Stochastic Processes)
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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. View Full-Text
Keywords: dynamical fluctuations; large deviations; stochastic thermodynamics; molecular dynamics dynamical fluctuations; large deviations; stochastic thermodynamics; molecular dynamics
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Jack, R.L.; Kaiser, M.; Zimmer, J. Symmetries and Geometrical Properties of Dynamical Fluctuations in Molecular Dynamics. Entropy 2017, 19, 562.

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