Non-Maxwellian Velocity Statistics in Supercooled Liquids and Their Possible Relation to Super-Arrhenius Viscosity

Abstract

For particles of fixed mass, classical equilibrium statistical mechanics dictates a Maxwellian velocity distribution determined solely by the temperature, regardless of the interactions, density, or structure. Supercooled glass forming liquids realize long lived metastable states that evade equilibrium crystallization and may thus violate assumptions underlying Maxwellian statistics. We numerically demonstrate that supercooled liquids can exhibit persistent non-Maxwellian velocity distributions with deviations connected to their exceptionally slow super-Arrhenius relaxation. Our work is motivated by a general result establishing that long lived metastable states may exhibit finite width distributions of intensive variables. A distribution of temperatures implies non-Maxwellian velocity statistics. We test this prediction by introducing stochastic thermostats that generate stationary states while, unlike conventional thermostats, not imposing Maxwellian velocity distributions. Simulations with these thermostats yield long lived states that have, by comparison to Maxwellian velocity distributions, an excess kurtosis $0<κ\lesssim0.3$. Crystallization is strongly impeded with increasing $κ$. In a minimal description, temperature fluctuations are characterized by a dimensionless width $\overline{A}$ with $κ\simeq3\overline{A}^{2}$. The nearly constant $\overline{A}$ (of an average value $0.08$ and standard deviation $0.03$) found in viscosity data collapse across $45$ glass formers and in specific heat signatures is consistent with kurtosis found in our simulations. Long time non-Maxwellian velocity statistics may thus link slow relaxation, transport, and thermodynamic measurements. Independent of the tested theory, the stochastic thermostats that we introduce offer a molecular dynamics route to non-Maxwellian velocity statistics.