Roberts, Bryan W. (2026) A New Origin for Entropy: Jauch’s Conservation Law and the Geometry of Thermodynamics. [Preprint]

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Abstract

A central question for the foundations of thermodynamics is which conceptual structures underpin the existence of entropy and temperature. Jauch claimed that entropy and temperature could be derived from a novel conservation law. This paper reconstructs the physics and mathematics of Jauch's claim and finds that his original proof is not valid. Remarkably, his theorem is still true. The alternative proof provided here uses geometric ideas from modern gauge theory, revealing a deep geometric structure in the heart of thermodynamics. This result also helps to settle an old debate by showing that entropy and temperature can be defined in a new, conceptually clear way without appeal to an irreversible assumption like the second law.

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Item Type:	Preprint
Creators:	Creators Email ORCID Roberts, Bryan W. b.w.roberts@lse.ac.uk 0000-0003-0548-1280
Keywords:	thermodynamics, entropy, gauge theory, holonomy, curvature
Subjects:	Specific Sciences > Physics Specific Sciences > Physics > Quantum Field Theory Specific Sciences > Physics > Statistical Mechanics/Thermodynamics Specific Sciences > Physics > Symmetries/Invariances
Depositing User:	Bryan W. Roberts
Date Deposited:	25 Mar 2026 12:30
Last Modified:	25 Mar 2026 12:30
Item ID:	28751
Subjects:	Specific Sciences > Physics Specific Sciences > Physics > Quantum Field Theory Specific Sciences > Physics > Statistical Mechanics/Thermodynamics Specific Sciences > Physics > Symmetries/Invariances
Date:	2026
URI:	https://philsci-archive.pitt.edu/id/eprint/28751

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