Preprint Article Version 1 This version not peer reviewed

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

Version 1 : Received: 19 September 2017 / Approved: 20 September 2017 / Online: 20 September 2017 (04:08:44 CEST)

A peer-reviewed article of this Preprint also exists.

Gupta, S.; Ruffo, S. Equilibration in the Nosé–Hoover Isokinetic Ensemble: Effect of Inter-Particle Interactions. Entropy 2017, 19, 544. Gupta, S.; Ruffo, S. Equilibration in the Nosé–Hoover Isokinetic Ensemble: Effect of Inter-Particle Interactions. Entropy 2017, 19, 544.

Journal reference: Entropy 2017, 19, 544
DOI: 10.3390/e19100544


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 aims 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.

Subject Areas

Hamiltonian systems; classical statistical mechanics; ensemble equivalence; long-range interacting systems

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