Anomalous effects of velocity rescaling algorithms: the flying ice cube effect revisited

TL;DR

This paper investigates the flying ice cube artifact in molecular dynamics, revealing that certain velocity rescaling algorithms violate the equipartition theorem, and demonstrates that the CSVR thermostat correctly preserves energy distribution by satisfying detailed balance.

Contribution

The study clarifies the causes of the flying ice cube effect and shows that the CSVR thermostat avoids this artifact, unlike simpler rescaling methods.

Findings

The flying ice cube effect results from violation of detailed balance.

Rescaling velocities to the canonical distribution prevents the artifact.

Popular thermostats like Berendsen violate the equipartition theorem.

Abstract

The flying ice cube effect is a molecular dynamics simulation artifact in which the use of velocity rescaling thermostats sometimes causes the violation of the equipartition theorem, affecting both structural and dynamic properties. The reason for this artifact and the conditions under which it occurs have not been fully understood. Since the flying ice cube effect was first demonstrated, a new velocity rescaling algorithm (the CSVR thermostat) has been developed and become popular without its effects on the equipartition theorem being truly known. Meanwhile, use of the simple velocity rescaling and Berendsen thermostat algorithms has not abated but has actually continued to grow. Here, we have calculated the partitioning of the kinetic energy between translational, rotational, and vibrational modes in simulations of diatomic molecules to explicitly determine whether the equipartition theorem is violated under different thermostats and while rescaling velocities to different kinetic energy distributions. We have found that the underlying cause of the flying ice cube effect is a violation of balance leading to systematic redistributions of kinetic energy under simple velocity rescaling and the Berendsen thermostat. When velocities are instead rescaled to the canonical ensemble's kinetic energy distribution, as is done with the CSVR thermostat, the equipartition theorem is not violated, and we show that the CSVR thermostat satisfies detailed balance. The critical necessity for molecular dynamics practitioners to abandon the use of popular yet incorrect velocity rescaling algorithms is underscored with an example demonstrating that the main result of a highly-cited study is entirely due to artifacts resulting from the study's use of the Berendsen thermostat.