On the Generalised Equipartition Law

Guido Magnano, Beniamino Valsesia

Published 2020-09-05Version 1

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.