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The Geometry of Thermodynamics III
Version 1
: Received: 5 July 2022 / Approved: 6 July 2022 / Online: 6 July 2022 (10:19:33 CEST)
How to cite: Velazquez, L.; Parker, M. C.; Jeynes, C. The Geometry of Thermodynamics III. Preprints 2022, 2022070096. https://doi.org/10.20944/preprints202207.0096.v1 Velazquez, L.; Parker, M. C.; Jeynes, C. The Geometry of Thermodynamics III. Preprints 2022, 2022070096. https://doi.org/10.20944/preprints202207.0096.v1
Abstract
We survey the main results emerging in the rapidly developing field that considers the
geometry of thermodynamics and statistical mechanics. Our ideas of stability depend on variational
principles – Maximum Entropy together with Least Action (and the isomorphic Least Exertion) – and
this stability (invariance in time) indicates the centrality of the geometries of the systems. We explore
a variety of examples of the application of thermodynamics in both macro- and micro-systems,
and propose that irreversibility is an intrinsic and fundamental property of the physical realm
(instead of being merely emergent). Using the concept of complex time, we examine the underlying
mathematical unity of quantum mechanics, statistical mechanics, and geometrical thermodynamics.
We show how the Planck and Boltzmann constants provide the fundamental quantum units for
the phenomenological characteristics of the two Noether-conserved quantities controlling overall
thermodynamic behaviour: respectively, energy and entropy production. We discuss the far-reaching
isomorphisms (between all of complex time, temperature and the system symmetry) that always
exist for Maximum Entropy systems, even as they exhibit either irreversible (dissipative, yet still
dynamically stable) or reversible (including stable and static geometries) behaviours.
Keywords
Quantitative geometrical thermodynamics; Entropic uncertainty relations; Complex time; Loschmidt paradox; actio-entropy
Subject
Physical Sciences, Thermodynamics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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