Violation of the virial theorem and generalized equipartition theorem for logarithmic oscillators serving as a thermostat

TL;DR

This study investigates the limitations of logarithmic oscillators as thermostats, revealing violations of the virial and generalized equipartition theorems, and their inability to sustain nonequilibrium steady states.

Contribution

It demonstrates that modified logarithmic oscillators violate fundamental thermodynamic theorems and cannot effectively function as thermostats in simulations.

Findings

Virial theorem is practically violated in modified log-oscillators.

Generalized equipartition theorem breaks down above a critical temperature.

Log-oscillators cannot maintain nonequilibrium steady states.

Abstract

A logarithmic oscillator has been proposed recently to serve as a thermostat recently since it has a peculiar property of infinite heat capacity according to the virial theorem. In order to examine its feasibility by numerical simulations, a modified logarithmic potential has been applied in previous studies to eliminate the singularity at origin. The role played by the modification has been elucidated in the present study. We argue that the virial theorem is practically violated for the modified log-oscillator illustrated by a linear dependence of kinetic temperature on energy. Furthermore, as far as a thermalized log-oscillator is concerned, the generalized equipartition theorem with respect to the position coordinate is broken if the temperature is higher than a critical temperature. Finally, we show that log-oscillators fail to serve as thermostats for its incapability of maintaining a nonequilibrium steady state even though their energy is appropriately assigned.