Configurational density of states of power-law potentials and the virial theorem in steady states

TL;DR

This paper derives the exact configurational density of states for particles with power-law interactions, confirming a constant heat capacity and extending the virial theorem's validity to general steady states beyond traditional ensembles.

Contribution

It provides an exact calculation of the configurational density of states for power-law potentials and demonstrates the virial theorem's applicability in broader steady-state contexts.

Findings

Configurational density of states computed exactly for power-law potentials.

Constant microcanonical heat capacity confirmed.

Virial theorem validated in general steady states.

Abstract

In this brief note, the configurational density of states of a system of particles interacting via power-law pair potentials is computed exactly. The result is consistent with a constant microcanonical heat capacity. The well-known form of the virial theorem for this class of systems is recovered using only the obtained configurational density of states, and shown to be valid beyond the canonical and microcanonical ensembles, in general steady states.