Statistical ensembles provide a conceptual framework within whichto obtain the average behaviour of physical systems.The extent to which a system interacts with its environment determines the appropriate statistical ensemble with which to describe its properties.Isolated systems are described by the microcanonical ensemble.The expression for the Boltzmann entropy acts as a bridge equation relating the thermodynamic quantity, the entropy, to a statistical mechanical quantity, the multiplicity of microstates.Other forms of entropy, the Gibbs and Shannon entropies, and the relation of entropy to irreversibility are discussed.

Following the discovery of the two laws of thermodynamics, theorists turned to the issue of finding an interpretation of the laws in terms of the atomic and molecular properties of the gases. Following Clausius's interpretation in terms of the kinetic theory of gases, Maxwell discovered the Maxwell velocity distribution and related it to Gaussian statistics. This marked the beginnings of statistical mechanics and the realisation that the law of increase of entropy has only a statistical validity. Out of these analysis Boltzmann and Gibbs created the discipline of statistical mechanics. The Gibbs entropy is also central to information theory.