On the definition of temperature in FPU systems

TL;DR

This paper challenges the traditional definition of temperature in FPU systems, proposing it should be linked to low frequency modes' energy rather than mean kinetic energy, especially when energy equipartition is not achieved.

Contribution

It introduces a new way to define temperature in FPU systems based on low frequency modes' energy, diverging from classical kinetic energy assumptions.

Findings

Temperature correlates with low frequency modes' energy.

Energy equipartition is not necessary for this temperature definition.

Traditional kinetic energy-based temperature is inadequate in certain FPU conditions.

Abstract

It is usually assumed, in classical statistical mechanics, that the temperature should coincide, apart from a suitable constant factor, with the mean kinetic energy of the particles. We show that this is not the case for \FPU systems, in conditions in which energy equipartition between the modes is not attained. We find that the temperature should be rather identified with the mean value of the energy of the low frequency modes.