Statistical mechanics is the theory that describes the behavior of macroscopic systems in terms of thermodynamic variables (such as the entropy, volume, average number of particles, etc.), using as a starting point the microscopic structure of the physical system of interest. The difference between thermodynamics and statistical mechanics is that the first theory is based on empirical observations, whereas the second theory is based on knowledge (true or assumed) of the microscopic constituents and their interactions. The similarity between the two theories is that they both address the macroscopic behavior of the system: thermodynamics does it by dealing exclusively with macroscopic quantities and using empirical laws, and statistical mechanics does it by constructing averages over all states consistent with the external conditions imposed on the system (such as temperature, pressure, chemical potential, etc.). Thus, the central theme in statistical mechanics is to identify all the possible states of the system in terms of their microscopic structure, and take an average of the physical quantities of interest over those states that are consistent with the external conditions. The average must involve the proper weight for each state, which is related to the likelihood of this state to occur, given the external conditions.

As in thermodynamics, statistical mechanics assumes that we are dealing with systems composed of a very large number of microscopic particles (typically atoms or molecules). The variables that determine the state of the system are the position, momentum, electric charge and magnetic moment of the particles. All these are microscopic variables, and their values determine the state of individual particles.