Statistical mechanics describes the thermodynamic behaviour of macroscopic systems from the laws which govern the behaviour of the constituent elements at the microscopic level. The microscopic elements can be atoms, molecules, dipole moments or magnetic moments, etc. A macroscopic system, generally, is composed of a large number of these elements (of the order of Avogadro number per mole). Each element may have a large number of internal degrees of freedom associated with different types of motion such as translation, rotation, vibration etc. The constituent elements may interact with the external field applied to the system. There can also be very complex interaction among the constituent elements. The macroscopic properties of a system is thus determined in the thermodynamic limit by the properties of the constituent molecules, their interaction with external field as well as interaction among themselves.

[ Thermodynamic limit: For a system of N elements of volume V and density ρ, the thermodynamic limit is defined as , keeping finite. In this limit, the extensive properties of the system become directly proportional to the size of the system ( N or V), while the intensive properties become independent of the size of the system.]

In the formalism of statistical mechanics, a macroscopic property of a system is obtained by taking a “statistical average” (or “ensemble average”) of the property over all possible “microstates” of the system. A microstate of a system is defined by specifying the states of all of its constituent elements.

Thermodynamic equilibrium of a system can be achieved in different ways depending upon the interaction of the system with the rest of the universe (heat bath, pressure bath, etc). Different external conditions leading to thermodynamic equilibrium of a system give rise to different ensembles. Once microstates and ensembles are specified, macroscopic quantities can be obtained by taking appropriate statistical averages corresponding to a given ensemble.