Dynamic Admissible States, Negative Absolute Temperature, and the Entropy Maximum Principle

Abstract

Gibbs ([1], p. 55) began his major memoir on thermostatics by the dictum of Clausius: “The energy of the universe is constant. The entropy of the universe tends to a maximum.” Replacing the “universe” of Clausius by a down-to-earth “isolated material system”, Gibbs saw the basis for what we now call his Entropy Maximum Principle, which he developed “as a foundation for the general theory of thermodynamic equilibrium” ([2], p. 354). Gibbs’s statement of his entropy principle was vague, but he also applied it (to be precise, here I should have said its companion Energy Minimum Principle, which Gibbs “preferred in general to use”) to a variety of systems. A general principle will assume appropriate specific forms in different concrete problems. On the other hand, after seeing how a vaguely worded, general principle has been used in various situations, we should be able to discern that which is in common. Thence it is no accident that van der Waals ([3], § 2) and Coleman & Noll ([4], § 16) should independently give the same formulation of the Entropy Maximum Principle for the same type of “isolated systems”, for what they gave is in essence Gibbs’s original formulation and they expressed it in the language of fields. The present essay is meant to be a critique of this formulation.