Microcanonical ensemble

The microcanonical ensemble is the simplest of the ensembles of statistical mechanics, in which each system of the ensmble is assumed to have the same total energy.

Classically, this means that every system within the ensemble is assumed to be confined to a region of phase space of constant energy. By application of Liouville's Theorem, if the replicas of the system are uniformly distributed through the accessible phase space initially, they will remain so at all future times.

Quantum mechanically, this means that every system within the ensemble is known to be in a quantum state of equal energy. The microcanonical partition function is simply the quantum degeneracy of the energy state corresponding to the fixed energy of the ensemble, usually denoted Ω. The thermodynamic potential governing the microcanonical ensemble is the entropy of the system, which is simply defined as:

S = k_BlnΩ

where:

S is the entropy of the ensemble,

k_B is the Boltzmann constant, and

Ω is the microcanonical partition function.

See also: Microcanonical ensemble, Boltzmann constant, Energy, Ensemble, Entropy, Liouville's theorem (Hamiltonian), Phase space, Physics, Quantum degeneracy