Classical Statistical Mechanics, Configuration, and Classical Canonical Partition Function

Abstract

To deeply grasp the physical significance of an activity, statistical thermodynamics must be considered and, in particular, it is the case of the notions of configuration of a system and of the classical canonical partition function.

Firstly, the chapter presents a definition of the configuration of a system. Secondly, the chapter is a presentation of the classical canonical partition function and of some relations stemming from it. It may be viewed as being an extension, in some definite conditions, of the canonical partition function occurring in quantum mechanics. All the mathematical terms constituting the function are presented. This is especially the case of the hamiltonian of the system. In some conditions, Hamilton’s function is nothing more or less than the energy of the system. It entails the kinetic energy of the whole particles constituting the system and their mutual interacting potential energy. A simple example of its handling, concerning perfect gases, is given at the end of the chapter.

The partition function, indeed, is the most used partition function in the field of applications of statistical thermodynamics to chemistry. The function will be quasi-systematically used until the end of the book. It is a physical parameter of first importance in the grasping of the significance of an activity.