Heat as a gauge connection

Abstract

We show that heat defines a gauge connection on a line bundle over work configurations. Vanishing curvature is equivalent to the local existence of entropy and temperature functions such that heat can be expressed as $TdS$. A conjecture of Jauch, that entropy and temperature arise from a conservation law, is shown to follow as a special case. Global equilibrium may nevertheless fail in the presence of a thermal analogue of geometric phase.