On the meaning of the canonical ensemble

Thermal equilibrium between (quantum) systems is taken to mean stability for the combined system. Necessary and sufficient conditions for such stability are found and used to show that any system in equilibrium with suitably complex second system (heat bath) will be characterized by a canonical ensemble. Thus the notion of temperature is derived directly from that of equilibrium, without, for example, recourse to microcanonical ensembles or information theory. Discussed briefly are the generalization of these results to grand canonical ensembles and their application to the equilibrium between a black hole and the surrounding radiation field.