Temperature in the classical microcanonical ensemble

Abstract

We show that a formula for the temperature of a classical system, originally given by Rugh, can be generalized. The result is that the inverse of the temperature is proportional to the average of the function ∇.(B/B.∇H), where H is the Hamiltonian of the system and B is an arbitrary vector function of the coordinates in phase space. Special cases of the new formula include a number of familiar results including the virial theorem.