Fundamental postulate of statistical mechanics

The fundamental postulate states that, for an isolated system in equilibrium, every microstate consistent with the system's fixed energy, volume, and particle number is equally likely. It is the single assumption on which the entire edifice of statistical mechanics rests: once microstates are equiprobable, the probability of a macrostate is simply its share of the total microstate count, Ω(macrostate)/Ω(total).

The postulate is sometimes called the assumption of 'equal a priori probabilities.' It is a statement of maximal ignorance — having no reason to prefer one accessible microstate over another, we assign them equal weight — and it defines the microcanonical ensemble. From it follow the Boltzmann entropy, the canonical Boltzmann distribution for systems in contact with a heat bath, and ultimately all of equilibrium thermodynamics.

Why the postulate works is subtle and connects to ergodic theory and the chaotic mixing of trajectories in phase space; for practical purposes its spectacular predictive success is its justification.

The principle is implicit in Boltzmann's ergodic hypothesis (1870s) and was given its modern ensemble formulation by J. Willard Gibbs in 'Elementary Principles in Statistical Mechanics' (1902).