The Statistical Mechanics of the Steady State

It is shown that the Fowler-Darwin definitions of the temperature and chemical potential can be extended in a natural way to cover non-equilibrium but steady assemblies. The concept of equilibrium is replaced by the more general one of `compatibility', and it becomes possible to show that the proposed statistical definitions of quantities like temperature reduce to suitable averages over the assembly of the locally measured quantities. The usual restrictions to small departures from equilibrium are unnecessary. A simple problem (flow of gas in a tube) is discussed from the new point of view.