Many physical processes, for example quantum processes such as nuclear reactions, are probabilistic, and can thus only be described statistically. The same consideration applies to many large classical systems that have so many variables, or degrees of freedom, that an exact treatment is not at all possible. Statistical physics can be used to model both of these types of systems. The development of the fundamental theory of statistical physics is chiefly credited to J. C. Maxwell, J. W. Gibbs, and L. E. Boltzmann for their contributions in both thermodynamics and mathematical formulation.

Statistical physics is divided into two main branches. The first is statistical mechanics, which attempts to predict the most probable behavior of a large collection of objects (an ensemble). Ensembles are characterized by specific macroscopic properties, such as volume, potential energy, pressure, and temperature. The individual particles in an ensemble, however, differ from each...