Finite-size and truncation effects for microscopic expressions for the temperature at equilibrium and nonequilibrium

Several expressions have been proposed for the temperature in molecular simulations, where some of them have configurational contributions. We investigate how their accuracy is influenced by the number of particles in the simulation and the discontinuity in the derivatives of the interaction potential introduced by truncation. For equilibrium molecular dynamics with fixed total volume and fixed average total energy per particle, all the evaluated expressions including that for the kinetic temperature give a dependence on the total number of particles in the simulation. However, in a partitioned simulation volume under the same conditions, the mean temperature of each bin is independent of the number of bins. This finding is important for consistently defining a local temperature for use in nonequilibrium simulations. We identify the configurational temperature expressions which agree most with the kinetic temperature and find that they give close to identical results in nonequilibrium molecular dynamics (NEMD) simulations with a temperature gradient, for high and low density bulk-systems (both for transient and steady-state conditions), and across vapor-liquid interfaces, both at equilibrium and during NEMD simulations. The work shows that the configurational temperature is equivalent to the kinetic temperature in steady-state molecular dynamics simulations if the discontinuity in the derivatives of the interaction potential is handled properly, by using a sufficiently long truncation-distance or tail-corrections.