An extension of Gibbs variational principle for canonical partition function

Abstract

Abstract

A variational principle is derived based upon the canonical partition functions. This variational principle is obtained using the Gibbs variational principle. Firstly, the Gibbs variational principle is highlighted for the canonical ensemble. Then, the Gibbs variational principle is modified such that a variational principle concerning the partition function is obtained. The latter variational principle is useful as the canonical partition function is an important quantity in deriving many thermodynamic quantities of a physical system based upon the distribution of the constituents that makes up the system.

Key words: variational principle, Gibbs variational principle, partition function