branch of physics that combines the principles and procedures of statistics with the laws of both classical and quantum mechanics, particularly with respect to the field of thermodynamics. It aims to predict and explain the measurable properties of macroscopic systems on the basis of the properties and behaviour of the microscopic constituents of those systems. Statistical mechanics interprets, for example, thermal energy as the energy of atomic particles in disordered states and temperature as a quantitative measure of how energy is shared among such particles. Statistical mechanics draws heavily on the laws of probability so that it does not concentrate on the behaviour of every individual particle in a macroscopic substance but on the average behaviour of a large number of particles of the same kind.

The mathematical structure of statistical mechanics was established by the American physicist Josiah Willard Gibbs (Gibbs, J Willard) in his book Elementary Principles in Statistical Mechanics (1902), but two earlier physicists, James Clerk Maxwell (Maxwell, James Clerk) of Great Britain and Ludwig E. Boltzmann (Boltzmann, Ludwig Eduard) of Austria, are generally credited with having developed the fundamental principles of the field with their work on thermodynamics. Over the years the methods of statistical mechanics have been applied to such phenomena as Brownian motion (i.e., the random movement of minute particles suspended in a liquid or gas) and electric conduction in solids. They also have been used in relating computer simulations of molecular dynamics to the properties of a wide range of fluids and solids.