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Geometry in Thermodynamics III

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Thermodynamics".

Deadline for manuscript submissions: closed (15 December 2023) | Viewed by 7696

Special Issue Editors


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Guest Editor
School of Computer Science and Electronic Engineering, University of Essex, Colchester CO4 3SQ, UK
Interests: quantitative geometrical thermodynamics (QGT); geometric entropy; maximum entropy (MaxEnt) theory; entropy production; info-entropy; thermodynamics of information; blackhole physics; dark matter; non-locality and entanglement; communications theory; quantum information; holograms and topological defects; fundamentals of quantum mechanics

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Guest Editor
Academic and research departments, Ion Beam Centre, University of Surrey, Guildford GU2 7XH, UK
Interests: quantitative geometrical thermodynamics; metrology; spectrometry; ion beam analysis; scientific epistemology; history of ideas

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Guest Editor
Physics Department, Universidad Católica del Norte, Antofagasta P.C. 124000, Chile
Interests: riemannian approaches in thermodynamics and statistical mechanics; generalized fluctuation theorems; dynamics and thermodynamics of systems with long-range interactions; astrophysics; computational physics; information theory; condensed matter; mathematical physics; complex systems; physics education

Special Issue Information

Dear Colleagues,

The role of entropy in dynamically shaping and organizing the natural structures, shapes and processes intrinsic to the universe is slowly becoming apparent. Rather than being a force for disorder and chaos, entropy is emerging as the underlying principle controlling the order and characteristic geometries frequently seen in nature. Entropy is emerging as the equal twin of energy: both are required to provide a comprehensive and mutually-complementary description of natural phenomena. Indeed, it is becoming clear that many of the currently intractable mysteries of contemporary science, including in the life sciences, might start to be unlocked with a proper understanding of the role that is played by geometrical thermodynamics at all scales (from the sub-atomic through to the molecular, macroscopic, and cosmological).

It is hoped that this Special Issue will provide a forum for the latest developments to be presented in this very wide and rapidly developing subject, as well as a platform to educate, inform and potentially surprise the scientific community with the explanatory power afforded by the science of geometrical thermodynamics. In particular, a new appreciation of geometry in thermodynamics is also expected to generate important insights into the epistemological interpretation of quantum mechanics and a new perspective for alternative descriptions of scientific reality.

Dr. Michael Parker
Prof. Dr. Christopher Jeynes
Dr. Luisberis Velazquez
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • geometric entropy
  • entropy production and maximum entropy production principle (MEPP)
  • isomorphism between kinematic (Planck) and entropic (Boltzmann) domains
  • holographic principle
  • blackhole physics
  • lagrangian/Hamiltonian variational formulations
  • noether conservation in lagrangian systems
  • quantum biology and irreversible processes in living systems
  • epistemology of quantum mechanics
  • non-locality and hidden variables

Published Papers (4 papers)

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Research

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19 pages, 337 KiB  
Article
Relating a System’s Hamiltonian to Its Entropy Production Using a Complex Time Approach
by Michael C. Parker and Chris Jeynes
Entropy 2023, 25(4), 629; https://doi.org/10.3390/e25040629 - 06 Apr 2023
Cited by 6 | Viewed by 1317
Abstract
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 [...] Read more.
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”. Full article
(This article belongs to the Special Issue Geometry in Thermodynamics III)
30 pages, 603 KiB  
Article
Thermodynamics of an Empty Box
by Georg J. Schmitz, Michael te Vrugt, Tore Haug-Warberg, Lodin Ellingsen, Paul Needham and Raphael Wittkowski
Entropy 2023, 25(2), 315; https://doi.org/10.3390/e25020315 - 08 Feb 2023
Viewed by 1866
Abstract
A gas in a box is perhaps the most important model system studied in thermodynamics and statistical mechanics. Usually, studies focus on the gas, whereas the box merely serves as an idealized confinement. The present article focuses on the box as the central [...] Read more.
A gas in a box is perhaps the most important model system studied in thermodynamics and statistical mechanics. Usually, studies focus on the gas, whereas the box merely serves as an idealized confinement. The present article focuses on the box as the central object and develops a thermodynamic theory by treating the geometric degrees of freedom of the box as the degrees of freedom of a thermodynamic system. Applying standard mathematical methods to the thermodynamics of an empty box allows equations with the same structure as those of cosmology and classical and quantum mechanics to be derived. The simple model system of an empty box is shown to have interesting connections to classical mechanics, special relativity, and quantum field theory. Full article
(This article belongs to the Special Issue Geometry in Thermodynamics III)
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27 pages, 407 KiB  
Article
An Alternative Study about the Geometry and the First Law of Thermodynamics for AdS Lovelock Gravity, Using the Definition of Conserved Charges
by Rodrigo Aros, Milko Estrada and Pablo Pereira
Entropy 2022, 24(9), 1197; https://doi.org/10.3390/e24091197 - 27 Aug 2022
Cited by 1 | Viewed by 1360
Abstract
In this work, we introduce an extension of the study of the first law of thermodynamics of black holes based on the geometry of the extended phase space for AdS Lovelock gravities, which includes changes in scales. As expected, the result obtained coincides [...] Read more.
In this work, we introduce an extension of the study of the first law of thermodynamics of black holes based on the geometry of the extended phase space for AdS Lovelock gravities, which includes changes in scales. As expected, the result obtained coincides with the previously known four-dimensional case. For higher dimensions, the result is the rise of two new contributions to the first law of thermodynamics. The first term corresponds to corrections of the usual definition of thermodynamic volumes at the horizon due to the presence of the higher curvature terms. The second term arises in odd dimensions, comes from the asymptotic region, and corresponds to a scale transformation of the form δ^ln(l/), with l the AdS radius and a parameter. A particularly interesting case corresponds to the Chern Simons gravity where the change scale does not generate a contribution at the asymptotic region, likely due to the Chern Simons AdS local symmetry. Full article
(This article belongs to the Special Issue Geometry in Thermodynamics III)

Review

Jump to: Research

10 pages, 864 KiB  
Review
How “Berry Phase” Analysis of Non-Adiabatic Non-Hermitian Systems Reflects Their Geometry
by Chris Jeynes
Entropy 2023, 25(2), 390; https://doi.org/10.3390/e25020390 - 20 Feb 2023
Cited by 1 | Viewed by 1675
Abstract
There is currently great interest in systems represented by non-Hermitian Hamiltonians, including a wide variety of real systems that may be dissipative and whose behaviour can be represented by a “phase” parameter that characterises the way “exceptional points” (singularities of various sorts) determine [...] Read more.
There is currently great interest in systems represented by non-Hermitian Hamiltonians, including a wide variety of real systems that may be dissipative and whose behaviour can be represented by a “phase” parameter that characterises the way “exceptional points” (singularities of various sorts) determine the system. These systems are briefly reviewed here with an emphasis on their geometrical thermodynamics properties. Full article
(This article belongs to the Special Issue Geometry in Thermodynamics III)
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