Microcanonical ensemble
An isolated system at fixed energy, volume and particle number, with every accessible microstate equally likely.
Definition
The microcanonical ensemble describes a completely isolated system whose energy E, volume V and particle number N are all fixed. Its founding postulate is that every microstate consistent with these constraints is equally probable. The entropy is then Boltzmann's S = k_B ln Ω, where Ω is the number of accessible microstates, and temperature, pressure and chemical potential emerge as derivatives of S.
It is the most fundamental of the three Gibbs ensembles, since it rests only on equal a priori probabilities and the conservation of energy, with no reservoir invoked. The canonical and grand canonical ensembles are derived from it by coupling a small subsystem to a large microcanonical reservoir.
In practice the microcanonical ensemble is often harder to compute with than the canonical one, because counting states at exactly one energy is more awkward than summing Boltzmann factors over all energies. For macroscopic systems the two give identical thermodynamics, so the choice is one of convenience.