First part of Clausius heat theorem in terms of Noether's theorem

Abstract

After Helmholtz, the mechanical foundation of thermodynamics included the First Law $dE=\delta Q+\delta W$, and the first part of the Clausius heat theorem $\delta Q^{\text{rev}}/T=dS$. The resulting invariance of the entropy $S$ for quasistatic changes in thermally isolated systems invites a connection with Noether's theorem (only established later). In this quest, we continue an idea, first brought up by Wald in black hole thermodynamics and by Sasa $\text{et al.}$ in various contexts. We follow both Lagrangian and Hamiltonian frameworks, and emphasize the role of Killing equations for deriving a First Law for thermodynamically consistent trajectories, to end up with an expression of ``heat over temperature'' as an exact differential of a Noether charge.

28 pages

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Cited by in corpus (1)

• Noether's theorem applied to GENERIC