Analysis of energy and friction coefficient fluctuations of a Lennard-Jones liquid coupled to the Nosé–Hoover thermostat

Thermal fluctuations of a many-body system coupled to a Nosé–Hoover thermostat depend on the strength of the coupling parameter τ*. A wrong choice may bring non-ergodic features and non-canonical fluctuations. Here, we analyse by means of molecular dynamics simulations both the energy fluctuations and the spectrum of the friction coefficient ζ^* of an extended Lennard-Jones system in a wide range of τ* at liquid density. Three ranges of τ* are identified – small, intermediate and large, plus their transitions. For τ* values in the intermediate range, ζ^* shows chaotic behaviour, and the particle system requires reasonable computing time for its thermalisation. As a result, the extended system is ergodic and energy fluctuations are canonical and stable in time. On the contrary, small and large ranges of τ* reveal clear evidence of periodicity in the thermostat variable, for instance by propagating the initial temperature condition. For these two ranges, the extended system shows non-ergodic features and energy fluctuations are non-canonical. For large τ*, micro-canonical fluctuations are occasionally obtained. For small to intermediate and intermediate to large ranges of τ*, the thermostat variable exhibits beat waves and is thus unable to reach equilibrium no matter how extended in time the simulations are. Here, we compare our results with previous work and explain the differences.