Introduction Statistical Mechanics is one of the fundamental branches of theoretical science. It concerns itself primarily with the prediction of the behavior of large numbers of atoms and molecules from the basic laws describing the interactions of small numbers of atoms or molecules. Within the broader field of theoretical chemistry, statistical mechanics occupies a central place between thermodynamics, which treats the behavior of bulk matter without reference to the possible validity of the atomic hypothesis, and quantum mechanics, which treats the electronic structure of single molecules but does not readily treat systems containing substantial numbers of unbonded atoms.
Statistical mechanics requires a description of the motions of individual atoms and molecules.
Such motions may be treated either with classical or quantum mechanics. However, modern chemistry and modern statistical mechanics largely treat systems in which the quantum nature of matter is not readily apparent, quantum theory only being invoked to generate a list of the allowed energies of the system. To calculate the shapes of molecules, the forces between them, or the stages of a chemical reaction, quantum mechanics is needed. The bulk of modern research in statistical mechanics has been based on classical statistics. While quantum topics appear below, we will primarily discuss classical statistical mechanics.