  Molecular dynamics simulations of a quasi-harmonic solid are conducted to
elucidate the meaning of temperature fluctuations in canonical systems and
validate a well-known but frequently contested equation predicting the mean
square of such fluctuations. The simulations implement two virtual and one
physical (natural) thermostat and examine the kinetic, potential and total
energy correlation functions in the time and frequency domains. The results
clearly demonstrate the existence of quasi-equilibrium states in which the
system can be characterized by a well-defined temperature that follows the
mentioned fluctuation equation. The emergence of such states is due to the wide
separation of timescales between thermal relaxation by phonon scattering and
slow energy exchanges with the thermostat. The quasi-equilibrium states exist
between these two timescales when the system behaves as virtually isolated and
equilibrium.
