Isoconfigurational thermostat

TL;DR

This paper introduces a holonomic constraint-based thermostat that enforces constant configurational temperature in equilibrium systems, exploring different equations of motion and their effects on phase space distributions.

Contribution

It presents three novel sets of equations of motion for configurational thermostats, each preserving different statistical ensembles and satisfying the temperature constraint.

Findings

Gauss' principle does not preserve the canonical distribution.

Modified Hamiltonian yields a restricted microcanonical distribution.

New equations produce a restricted canonical ensemble with constant configurational temperature.

Abstract

A holonomic constraint is used to enforce a constant instantaneous configurational temperature on an equilibrium system. Three sets of equations of motion are obtained, differing according to the way in which the holonomic constraint is introduced and the phase space distribution function that is preserved by the dynamics. Firstly, Gauss' principle of least constraint is used, and it is shown that it does not preserve the canonical distribution. Secondly, a modified Hamiltonian is used to find a dynamics that provides a restricted microcanonical distribution. Lastly, we provide equations that are specifically designed to both satisfy the temperature constraint and produce a restricted canonical ensemble.