 Microcanonical ensemble

The microcanonical ensemble describes an isolated equilibrium system with fixed volume, particle number and energy within a narrow shell. It assigns equal probability to the accessible microstates inside that shell. For a discrete count $\Omega (E)$, the entropy is $S=k_B\log \Omega$; classical phase-space counting also requires a specified measure and shell width.

An idealized insulated rigid container motivates the constraints. Its particles exchange energy internally, but the whole container exchanges neither heat nor particles with its surroundings. A small subsystem can still have fluctuating energy because the rest acts as a reservoir. In the thermodynamic regime where that reservoir has a well-defined temperature, the subsystem approaches a canonical ensemble. Equal shell probabilities are an ensemble prescription; whether a particular dynamics explores the accessible shell on an experimental timescale is a separate equilibration question.