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Entropy
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Geometry in Thermodynamics, 4th Edition
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Geometry in Thermodynamics, 4th Edition

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

Deadline for manuscript submissions: 31 January 2026 | Viewed by 2209

Special Issue Editors

Dr. Michael Parker

E-Mail Website
Guest Editor
School of Computer Science and Electronic Engineering, University of Essex, Colchester CO4 3SQ, UK
Interests: quantitative geometrical thermodynamics (QGTs); 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
Special Issues, Collections and Topics in MDPI journals
Dr. Chris Jeynes
*
E-Mail Website
Guest Editor
Independent Researcher, Tredegar NP22 4LP, UK
Interests: quantitative geometrical thermodynamics; metrology; spectrometry; ion beam analysis; scientific epistemology; history of ideas
* Formerly at University of Surrey Ion Beam Centre, Guildford GU2 7XH, UK
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Stuart Walker

E-Mail Website
Guest Editor
School of Computer Sciences and Electronic Engineering, University of Essex, Colchester CO4 3SQ, UK
Interests: maximum entropy (MaxEnt) theory; entropy production; info-entropy; thermodynamics of information; communications theory; quantum information; fundamentals of quantum mechanics; network optimisation; analogue/digital electronics; circuit simulation and realisation
Dr. Luisberis Velazquez

E-Mail Website
Guest Editor
Physics Department, Universidad Católica del Norte, Antofagasta 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 Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The prominent role of entropy in dynamically shaping and organising natural structures, shapes, and processes intrinsic to the universe, as well as their temporal evolution, is now very clear. Thermodynamics is emerging as the underlying principle controlling the order and characteristic geometries frequently seen in nature, as well as determining their rate of evolution and change. Entropy production is complementary to energy: both are required to provide a comprehensive description of natural phenomena, and both are conserved in any dynamic process. Spacetime must be fully complexified (Ivo Dinov calls this “5D spacekime”) to successfully integrate energy and entropy production into a complementary and unified physical description.

It is hoped that this Special Issue will provide a forum for the latest developments to be presented in the very wide and rapidly developing subject of geometrical thermodynamics. We hope that the science of geometrical thermodynamics as applied to dissipative and non-dissipative processes will continue to provide new physical insights based on unified entropic and kinematic principles, new understandings of physical processes, and a new perspective for a more complete description of scientific reality.

Dr. Michael Parker
Dr. Chris Jeynes
Prof. Dr. Stuart Walker
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 250 words) can be sent to the Editorial Office for assessment.

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

  • thermodynamic time
  • complex time
  • entropy production
  • dissipative processes and structures
  • conservation theorems
  • local and non-local constraints
  • thermodynamics of information
  • system complexity
  • Riemannian geometries
  • generalised fluctuation theorems
  • dynamics and thermodynamics of systems with long-range interactions

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Published Papers (2 papers)

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Research

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24 pages, 756 KB  
Article
Complex Time Approach to the Hamiltonian and the Entropy Production of the Damped Harmonic Oscillator
by Kyriaki-Evangelia Aslani
Entropy 2025, 27(8), 883; https://doi.org/10.3390/e27080883 - 21 Aug 2025
Cited by 1 | Viewed by 1452
Abstract
The present work applies and extends the previously developed Quantitative Geometrical Thermodynamics (QGT) formalism to the derivation of a Hamiltonian for the damped harmonic oscillator (DHO) across all damping regimes. By introducing complex time, with the real part encoding entropy production and the [...] Read more.
The present work applies and extends the previously developed Quantitative Geometrical Thermodynamics (QGT) formalism to the derivation of a Hamiltonian for the damped harmonic oscillator (DHO) across all damping regimes. By introducing complex time, with the real part encoding entropy production and the imaginary part governing reversible dynamics, QGT provides a unified geometric framework for irreversible thermodynamics, showing that the DHO Hamiltonian can be obtained directly from the (complex) entropy production in a simple exponential form that is generalized across all damping regimes. The derived Hamiltonian preserves a modified Poisson bracket structure and embeds thermodynamic irreversibility into the system’s evolution. Moreover, the resulting expression coincides in form with the well-known Caldirola–Kanai Hamiltonian, despite arising from fundamentally different principles, reinforcing the validity of the QGT approach. The results are also compared with the GENERIC framework, showing that QGT offers an elegant alternative to existing approaches that maintains consistency with symplectic geometry. Furthermore, the imaginary time component is interpreted as isomorphic to the antisymmetric Poisson matrix through the lens of geometric algebra. The formalism opens promising avenues for extending Hamiltonian mechanics to dissipative systems, with potential applications in nonlinear dynamics, quantum thermodynamics, and spacetime algebra. Full article
(This article belongs to the Special Issue Geometry in Thermodynamics, 4th Edition)
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Review

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22 pages, 2682 KB  
Review
Unitary Entities Are the True “Atoms”
by Chris Jeynes and Michael Charles Parker
Entropy 2025, 27(11), 1119; https://doi.org/10.3390/e27111119 - 30 Oct 2025
Viewed by 348
Abstract
Quantitative Geometrical Thermodynamics (QGT) exploits the entropic Lagrangian–Hamiltonian canonical equations of state as applied to entities obeying the holographic principle and exhibiting Shannon information, the creation of which measures the (validly defined) “entropic purpose” of the system. QGT provides a physical description for [...] Read more.
Quantitative Geometrical Thermodynamics (QGT) exploits the entropic Lagrangian–Hamiltonian canonical equations of state as applied to entities obeying the holographic principle and exhibiting Shannon information, the creation of which measures the (validly defined) “entropic purpose” of the system. QGT provides a physical description for what we might consider the true “atoms” of physical science and has also recently enabled a number of significant advances: accounting ab initio for the chirality of DNA and the stability of Buckminsterfullerene; the size of the alpha particle (and other nuclear entities) and the lifetime of the free neutron; and the shape, structure, and stability of the Milky Way galaxy. All these entities, ranging in size over more than 38 orders of magnitude, can each be considered to be an “atom”; in particular, the size of the alpha is calculated from QGT by assuming that the alpha is a “unitary entity” (that is, than which exists no simpler). The surprising conclusion is that clearly compound entities may also be physically treated as unitary (“uncuttable”) according to a principle of scale relativity, where a characteristic size for such an entity must be specified. Since QGT is entropic, and is therefore described using a logarithmic metric (involving hyperbolic space), it is not surprising that the length scale must be specified in order to account for unitary properties and for an entity to be appropriately considered an “atom”. The contribution to physics made by QGT is reviewed in the context of the related work of others. Full article
(This article belongs to the Special Issue Geometry in Thermodynamics, 4th Edition)
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