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Open AccessArticle

Equilibration in the Nosé–Hoover Isokinetic Ensemble: Effect of Inter-Particle Interactions

1
Department of Physics, Ramakrishna Mission Vivekananda University, Belur Math, Howrah 711202, India
2
SISSA, INFN and ISC-CNR, Via Bonomea 265, I-34136 Trieste, Italy
*
Author to whom correspondence should be addressed.
Entropy 2017, 19(10), 544; https://doi.org/10.3390/e19100544
Received: 19 September 2017 / Revised: 11 October 2017 / Accepted: 11 October 2017 / Published: 14 October 2017
(This article belongs to the Special Issue Thermodynamics and Statistical Mechanics of Small Systems)
We investigate the stationary and dynamic properties of the celebrated Nosé–Hoover dynamics of many-body interacting Hamiltonian systems, with an emphasis on the effect of inter-particle interactions. To this end, we consider a model system with both short- and long-range interactions. The Nosé–Hoover dynamics aim to generate the canonical equilibrium distribution of a system at a desired temperature by employing a set of time-reversible, deterministic equations of motion. A signature of canonical equilibrium is a single-particle momentum distribution that is Gaussian. We find that the equilibrium properties of the system within the Nosé–Hoover dynamics coincides with that within the canonical ensemble. Moreover, starting from out-of-equilibrium initial conditions, the average kinetic energy of the system relaxes to its target value over a size-independent timescale. However, quite surprisingly, our results indicate that under the same conditions and with only long-range interactions present in the system, the momentum distribution relaxes to its Gaussian form in equilibrium over a scale that diverges with the system size. On adding short-range interactions, the relaxation is found to occur over a timescale that has a much weaker dependence on system size. This system-size dependence of the timescale vanishes when only short-range interactions are present in the system. An implication of such an ultra-slow relaxation when only long-range interactions are present in the system is that macroscopic observables other than the average kinetic energy when estimated in the Nosé–Hoover dynamics may take an unusually long time to relax to its canonical equilibrium value. Our work underlines the crucial role that interactions play in deciding the equivalence between Nosé–Hoover and canonical equilibrium. View Full-Text
Keywords: Hamiltonian systems; classical statistical mechanics; ensemble equivalence; long-range interacting systems Hamiltonian systems; classical statistical mechanics; ensemble equivalence; long-range interacting systems
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Gupta, S.; Ruffo, S. Equilibration in the Nosé–Hoover Isokinetic Ensemble: Effect of Inter-Particle Interactions. Entropy 2017, 19, 544.

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