First part of Clausius heat theorem in terms of Noether's theorem
| Autor: | Beyen, Aaron, Maes, Christian |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | After Helmholtz, the mechanical foundation of thermodynamics included the First Law $d E = \delta Q + \delta W$, 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 $\textit{et al.}$ 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. Comment: 26 pages |
| Databáze: | arXiv |
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