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Relating a System’s Hamiltonian to Its Entropy Production Using a Complex Time Approach

We exploit the properties of complex time to obtain an analytical relationship based on considerations of causality between the two Noether-conserved quantities of a system: its Hamiltonian and its entropy production. In natural units, when complexified, the one is simply the Wick-rotated complex co...

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Autores principales: Parker, Michael C., Jeynes, Chris
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10137557/
https://www.ncbi.nlm.nih.gov/pubmed/37190417
http://dx.doi.org/10.3390/e25040629
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author Parker, Michael C.
Jeynes, Chris
author_facet Parker, Michael C.
Jeynes, Chris
author_sort Parker, Michael C.
collection PubMed
description We exploit the properties of complex time to obtain an analytical relationship based on considerations of causality between the two Noether-conserved quantities of a system: its Hamiltonian and its entropy production. In natural units, when complexified, the one is simply the Wick-rotated complex conjugate of the other. A Hilbert transform relation is constructed in the formalism of quantitative geometrical thermodynamics, which enables system irreversibility to be handled analytically within a framework that unifies both the microscopic and macroscopic scales, and which also unifies the treatment of both reversibility and irreversibility as complementary parts of a single physical description. In particular, the thermodynamics of two unitary entities are considered: the alpha particle, which is absolutely stable (that is, trivially reversible with zero entropy production), and a black hole whose unconditional irreversibility is characterized by a non-zero entropy production, for which we show an alternate derivation, confirming our previous one. The thermodynamics of a canonical decaying harmonic oscillator are also considered. In this treatment, the complexification of time also enables a meaningful physical interpretation of both “imaginary time” and “imaginary energy”.
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spelling pubmed-101375572023-04-28 Relating a System’s Hamiltonian to Its Entropy Production Using a Complex Time Approach Parker, Michael C. Jeynes, Chris Entropy (Basel) Article We exploit the properties of complex time to obtain an analytical relationship based on considerations of causality between the two Noether-conserved quantities of a system: its Hamiltonian and its entropy production. In natural units, when complexified, the one is simply the Wick-rotated complex conjugate of the other. A Hilbert transform relation is constructed in the formalism of quantitative geometrical thermodynamics, which enables system irreversibility to be handled analytically within a framework that unifies both the microscopic and macroscopic scales, and which also unifies the treatment of both reversibility and irreversibility as complementary parts of a single physical description. In particular, the thermodynamics of two unitary entities are considered: the alpha particle, which is absolutely stable (that is, trivially reversible with zero entropy production), and a black hole whose unconditional irreversibility is characterized by a non-zero entropy production, for which we show an alternate derivation, confirming our previous one. The thermodynamics of a canonical decaying harmonic oscillator are also considered. In this treatment, the complexification of time also enables a meaningful physical interpretation of both “imaginary time” and “imaginary energy”. MDPI 2023-04-06 /pmc/articles/PMC10137557/ /pubmed/37190417 http://dx.doi.org/10.3390/e25040629 Text en © 2023 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Parker, Michael C.
Jeynes, Chris
Relating a System’s Hamiltonian to Its Entropy Production Using a Complex Time Approach
title Relating a System’s Hamiltonian to Its Entropy Production Using a Complex Time Approach
title_full Relating a System’s Hamiltonian to Its Entropy Production Using a Complex Time Approach
title_fullStr Relating a System’s Hamiltonian to Its Entropy Production Using a Complex Time Approach
title_full_unstemmed Relating a System’s Hamiltonian to Its Entropy Production Using a Complex Time Approach
title_short Relating a System’s Hamiltonian to Its Entropy Production Using a Complex Time Approach
title_sort relating a system’s hamiltonian to its entropy production using a complex time approach
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10137557/
https://www.ncbi.nlm.nih.gov/pubmed/37190417
http://dx.doi.org/10.3390/e25040629
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