  So what role did the ergodic hypothesis play? It seems that Boltzmann regarded the ergodic hypothesis as a special dynamical assumption that may or may not be true, depending on the nature of the system, and perhaps also on its initial state. Its role was simply to help derive a result of great generality: for any system for which the hypothesis is true, its unique equilibrium state is characterized by the microcanonical distribution (3), from which a form of the Maxwell distribution may be recovered in the limit \(N \rightarrow \infty\), regardless of any details of the inter-particle interactions, or indeed whether the system represented is a gas, fluid, solid or any other thermal body.  Note also that the microcanonical distribution immediately implies that the probability of finding the system in any region on the energy hypersurface is proportional to the size of that region (as measured by the microcanonical measure). This idea would resurface in his 1877 combinatorial argument, although then without the context of characterizing equilibrium thermal equilibrium.