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2 Computational Methods in Science and Technology

2 2017

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Non-monotonic Relaxation in a HarmonicWell

King M. R., Jepps O. G.

Computational Methods in Science and Technology

2017

Vol. 23, No. 3

199--209

The dissipation function of Evans and Searles has its origins in describing entropy production, yet it has a straightforward dynamical interpretation as well. The ability to consider either dynamical or thermodynamical contexts deepens our understanding of the dissipation function as a concept, and of numerical results involving the dissipation function. One recent, important application of the dissipation function is in relaxation to equilibrium. Here we look at relaxation in a system of interacting molecules that are confined within a harmonic potential, undergoing Hamiltonian dynamics. We note some similarities, but also important differences, to previous studies. The dissipation function sheds light on the periodic return of our system towards its initial state.We find that intermolecular interactions play a much more significant role in the relaxation toward a non-uniform spatial distribution (induced by a conservative background field) than they do toward a uniform distribution, which is reflected in the strongly non-monotonic relaxation we observe. We also find that the maximum dissipation does not occur in the long-time limit, as one might expect of a relaxation process, but shortly after relaxation begins, beyond which a significant net overall decrease in the dissipation function is observed.

Ergodicity of non-Hamiltonian Equilibrium Systems

Evans D. J., Williams S. R., Rondoni L., Searles D. J.

Computational Methods in Science and Technology

2017

Vol. 23, No. 3

175--184

It is well known that ergodic theory can be used to formally prove a form of relaxation to microcanonical equilibrium for finite, mixing Hamiltonian systems. In this manuscript we substantially modify this proof using an approach similar to that used in umbrella sampling, and use this approach to consider relaxation in both Hamiltonian and non- Hamiltonian systems. In doing so, we demonstrate the need for a form of ergodic consistency of the initial and final distribution. The approach only applies to relaxation of averages of physical properties and low order probability distribution functions. It does not provide any information about whether the full 6N-dimensional phase space distribution relaxes towards the equilibrium distribution or how long the relaxation of physical averages takes.