New observations regarding deterministic, time reversible thermostats and Gauss's principle of least constraint

TL;DR

This paper demonstrates that the Gaussian isokinetic thermostat uniquely minimizes phase space compression, satisfies the conjugate pairing rule, and is the only thermostat that permits equilibrium states among various deterministic thermostats.

Contribution

The paper provides the first convincing arguments establishing the uniqueness of the Gaussian thermostat based on phase space compression and the conjugate pairing rule.

Findings

Gaussian thermostat minimizes phase space compression

It is the only thermostat satisfying the conjugate pairing rule

All other thermostats perform work like dissipative fields and are auto-dissipative

Abstract

Deterministic thermostats are frequently employed in non-equilibrium molecular dynamics simulations in order to remove the heat produced irreversibly over the course of such simulations. The simplest thermostat is the Gaussian thermostat, which satisfies Gauss's principle of least constraint and fixes the peculiar kinetic energy. There are of course infinitely many ways to thermostat systems, e.g. by fixing $\sum\limits_i{|{p_i}|^{\mu + 1}}$. In the present paper we provide, for the first time, convincing arguments as to why the conventional Gaussian isokinetic thermostat ($\mu=1$) is unique in this class. We show that this thermostat minimizes the phase space compression and is the only thermostat for which the conjugate pairing rule (CPR) holds. Moreover it is shown that for finite sized systems in the absence of an applied dissipative field, all other thermostats ($\mu=1$) perform work on the system in the same manner as a dissipative field while simultaneously removing the dissipative heat so generated. All other thermostats ($\mu=1$) are thus auto-dissipative. Among all $\mu$-thermostats, only the $\mu=1$ Gaussian thermostat permits an equilibrium state.