On the Generalised Equipartition Law

TL;DR

This paper identifies limitations in the traditional Generalised Equipartition Law for nonlinear Hamiltonian systems, introduces a new coordinate-independent generalisation, and demonstrates its broader applicability through an example.

Contribution

The paper proposes a new coordinate-independent generalisation of the Generalised Equipartition Law that extends its validity to a wider class of functions and nonlinear systems.

Findings

Traditional law has limited applicability due to omitted hypotheses.

New generalisation overcomes coordinate dependence issues.

Example illustrates broader applicability.

Abstract

We observe that the so-called Generalised Equipartition Law for hamiltonian systems is actually valid only under specific hypotheses -- unfortunately omitted in some textbooks -- which limit its applicability when dealing with nonlinear systems. We introduce a new coordinate-independent generalisation which overcomes this problem, and moreover can be applied to a larger set of functions. A simple example of application is discussed.