Anomalous fluctuations in low-temperature molecular dynamics simulations

We present results of a standard (constant energy) molecular dynamics simulation of Lennard-Jones micro-crystals at low temperature. The kinetic energy fluctuations exhibit an anomalous behavior, being much larger than expected in a microcanonical ensemble; this is due to a dynamics, which is only weakly chaotic. Such a dynamics does not warrant the equivalence of time and ensemble averages, unless one extends the simulation over exceedingly long times. A similar phenomenon has been recently found in the simulation of a canonical ensemble through a Nose-Hoover dynamics.