Thermodynamic Entropy as a Noether Invariant from Contact Geometry

Bravetti, Alessandro; García-Ariza, Miguel Ángel; Tapias, Diego

doi:10.3390/e25071082

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Thermodynamic Entropy as a Noether Invariant from Contact Geometry

by

Alessandro Bravetti

^1,*

,

Miguel Ángel García-Ariza

¹

and

Diego Tapias

²

¹

Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de Mexico, A. P. 70543, Ciudad de Mexico 04510, Mexico

²

Institute for Theoretical Physics, University of Göttingen, 37073 Göttingen, Germany

^*

Author to whom correspondence should be addressed.

Entropy 2023, 25(7), 1082; https://doi.org/10.3390/e25071082

Submission received: 30 June 2023 / Revised: 13 July 2023 / Accepted: 17 July 2023 / Published: 19 July 2023

(This article belongs to the Special Issue Geometric Structure of Thermodynamics: Theory and Applications)

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Abstract

We use a formulation of Noether’s theorem for contact Hamiltonian systems to derive a relation between the thermodynamic entropy and the Noether invariant associated with time-translational symmetry. In the particular case of thermostatted systems at equilibrium, we show that the total entropy of the system plus the reservoir are conserved as a consequence thereof. Our results contribute to understanding thermodynamic entropy from a geometric point of view.

Keywords: Noether’s theorem; Hamiltonian systems; contact geometry; entropy; thermostatted systems

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MDPI and ACS Style

Bravetti, A.; García-Ariza, M.Á.; Tapias, D. Thermodynamic Entropy as a Noether Invariant from Contact Geometry. Entropy 2023, 25, 1082. https://doi.org/10.3390/e25071082

AMA Style

Bravetti A, García-Ariza MÁ, Tapias D. Thermodynamic Entropy as a Noether Invariant from Contact Geometry. Entropy. 2023; 25(7):1082. https://doi.org/10.3390/e25071082

Chicago/Turabian Style

Bravetti, Alessandro, Miguel Ángel García-Ariza, and Diego Tapias. 2023. "Thermodynamic Entropy as a Noether Invariant from Contact Geometry" Entropy 25, no. 7: 1082. https://doi.org/10.3390/e25071082

APA Style

Bravetti, A., García-Ariza, M. Á., & Tapias, D. (2023). Thermodynamic Entropy as a Noether Invariant from Contact Geometry. Entropy, 25(7), 1082. https://doi.org/10.3390/e25071082

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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Thermodynamic Entropy as a Noether Invariant from Contact Geometry

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