Thermostatting nonequilibrium systems: A thermal energy constraint for systems under directive perturbations

This paper brings attention back to discussions about the use of equilibrium thermostats for nonequilibrium molecular dynamics simulations. It argues that, due to the fluctuation-dissipation theorem, the justification for using equilibrium thermostats for nonequilibrium simulations is inherited only by cases in which the perturbation is small enough for the perturbed system to behave like the unperturbed equilibrium system. In the process, this paper categorizes models of external perturbations in molecular dynamics as either responsive-i.e., perturbations that impose a force-or directive-i.e., perturbations that impose a trajectory. Since directive perturbations have not been studied enough in the literature but are becoming more relevant, their effects on simple perturbed thermostatted systems are considered. Finally, using a perturbed two-point harmonic oscillator as well as a driven particle immersed in a simple Lennard-Jones fluid, it gives an approximation for the limit of justified equilibrium thermostat use for perturbed systems. This paper hopes to inspire further research in the fields of nonequilibrium statistical mechanics and nonequilibrium molecular dynamics.