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Insight into Entropy
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Insight into Entropy

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

Deadline for manuscript submissions: 30 November 2025 | Viewed by 2174

Special Issue Editors

Prof. Dr. Philip Broadbridge

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Guest Editor
Department of Mathematical and Physical Sciences, La Trobe University Melbourne, Melbourne, VIC 3086, Australia
Interests: concepts of entropy and their applications; nonlinear diffusion
Special Issues, Collections and Topics in MDPI journals
Dr. Tony C. Scott

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Guest Editor
Institute of Physical Chemistry, RWTH Aachen University, 52056 Aachen, Germany
Interests: quantum gravity; superfluids; Bose–Einstein condensates; hybrid-symbolic numerics; computational physics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Entropy is a paramount concept. It can be a measure of width of a distribution, and it is often related to the level of chaos or randomness in a system. It is one of the most important concepts in physics and in information theory. The second law of thermodynamics states that entropy always increases (never decreases) in any process. It is transcendental in that it is a key component of entropic or emergent gravity but anthropomorphic in that it requires human notions of measure, disorder and cost.  Thus, it is not surprising that we have different mathematical assessments of entropy from different disciplines, including theoretical Physics, Biology, Cosmology and Economics:

  • Von Neumann entropy;
  • Everett–Hirschman entropy also called “entropic uncertainty”;
  • Information or Shannon entropy or differential entropy;
  • Algorithmic entropy (Kolmogorov complexity);
  • Rényi entropy (min-entropy);
  • Tsallis entropy, etc.

This Special Issue welcomes efforts in integrating these various definitions of entropy and/or finding out more about them so as to increase our insight into the very concept of entropy. There is likely no unique definition of entropy, but insight can be derived from connections and comparisons between these definitions and/or increased understanding from the individual concepts. Special attention will be focused on applications in quantum theory.

Prof. Dr. Philip Broadbridge
Dr. Tony C. Scott
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

  • Everett–Hirschman entropy
  • Von Neumann entropy
  • Shannon entropy
  • Rényi entropy
  • Tsallis entropy
  • quantum theory
  • nonlinear optics
  • logarithmic Schrödinger equation
  • superfluids
  • superconductors
  • emergent gravity

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (3 papers)

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Research

18 pages, 1438 KiB  
Article
Maximum Entropy Estimates of Hubble Constant from Planck Measurements
by David P. Knobles and Mark F. Westling
Entropy 2025, 27(7), 760; https://doi.org/10.3390/e27070760 - 16 Jul 2025
Viewed by 236
Abstract
A maximum entropy (ME) methodology was used to infer the Hubble constant from the temperature anisotropies in cosmic microwave background (CMB) measurements, as measured by the Planck satellite. A simple cosmological model provided physical insight and afforded robust statistical sampling of a parameter [...] Read more.
A maximum entropy (ME) methodology was used to infer the Hubble constant from the temperature anisotropies in cosmic microwave background (CMB) measurements, as measured by the Planck satellite. A simple cosmological model provided physical insight and afforded robust statistical sampling of a parameter space. The parameter space included the spectral tilt and amplitude of adiabatic density fluctuations of the early universe and the present-day ratios of dark energy, matter, and baryonic matter density. A statistical temperature was estimated by applying the equipartition theorem, which uniquely specifies a posterior probability distribution. The ME analysis inferred the mean value of the Hubble constant to be about 67 km/sec/Mpc with a conservative standard deviation of approximately 4.4 km/sec/Mpc. Unlike standard Bayesian analyses that incorporate specific noise models, the ME approach treats the model error generically, thereby producing broader, but less assumption-dependent, uncertainty bounds. The inferred ME value lies within 1σ of both early-universe estimates (Planck, Dark Energy Signal Instrument (DESI)) and late-universe measurements (e.g., the Chicago Carnegie Hubble Program (CCHP)) using redshift data collected from the James Webb Space Telescope (JWST). Thus, the ME analysis does not appear to support the existence of the Hubble tension. Full article
(This article belongs to the Special Issue Insight into Entropy)
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17 pages, 10694 KiB  
Article
Entropy-Inspired Aperture Optimization in Fourier Optics
by Marcos Miotti and Daniel Varela Magalhães
Entropy 2025, 27(7), 730; https://doi.org/10.3390/e27070730 - 7 Jul 2025
Viewed by 188
Abstract
The trade-off between resolution and contrast is a transcendental problem in optical imaging, spanning from artistic photography to technoscientific applications. To the latter, Fourier-optics-based filters, such as the 4f system, are well-known for their image-enhancement properties, removing high spatial frequencies from an [...] Read more.
The trade-off between resolution and contrast is a transcendental problem in optical imaging, spanning from artistic photography to technoscientific applications. To the latter, Fourier-optics-based filters, such as the 4f system, are well-known for their image-enhancement properties, removing high spatial frequencies from an optically Fourier-transformed light signal through simple aperture adjustment. Nonetheless, assessing the contrast–resolution balance in optical imaging remains a challenging task, often requiring complex mathematical treatment and controlled laboratory conditions to match theoretical predictions. With that in mind, we propose a simple yet robust analytical technique to determine the optimal aperture in a 4f imaging system for static and quasi-static objects. Our technique employs the mathematical formalism of the H-theorem, enabling us to directly access the information of an imaged object. By varying the aperture at the Fourier plane of the 4f system, we have empirically found an optimal aperture region where the imaging entropy is maximum, given that the object is fitted to the imaged area. At that region, the image is lit and well-resolved, and no further aperture decrease improves that, as information of the whole assembly (object plus imaging system) is maximum. With that analysis, we have also been able to investigate how the imperfections in an object affect the entropy during its imaging. Despite its simplicity, our technique is generally applicable and passable for automation, making it interesting for many imaging-based optical devices. Full article
(This article belongs to the Special Issue Insight into Entropy)
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14 pages, 1997 KiB  
Article
Shannon Entropy Analysis of a Nuclear Fuel Pin Under Deep Burnup
by Wojciech R. Kubiński, Jan K. Ostrowski and Krzysztof W. Fornalski
Entropy 2024, 26(12), 1124; https://doi.org/10.3390/e26121124 - 22 Dec 2024
Viewed by 1041
Abstract
This paper analyzes the behavior of the entropy of a nuclear fuel rod under deep burnup conditions, beyond standard operational ranges, reaching up to 60 years. The evolution of the neutron source distribution in a pressurized water reactor (PWR) fuel pin was analyzed [...] Read more.
This paper analyzes the behavior of the entropy of a nuclear fuel rod under deep burnup conditions, beyond standard operational ranges, reaching up to 60 years. The evolution of the neutron source distribution in a pressurized water reactor (PWR) fuel pin was analyzed using the Monte Carlo method and Shannon information entropy. To maintain proper statistics, a novel scaling method was developed, adjusting the neutron population based on the fission rate. By integrating reactor physics with information theory, this work aimed at the deeper understanding of nuclear fuel behavior under extreme burnup conditions. The results show a “U-shaped” entropy evolution: an initial decrease due to self-organization, followed by stabilization and eventual increase due to degradation. A minimum entropy state is reached after approximately 45 years of pin operation, showing a steady-state condition with no entropy change. This point may indicate a physical limit for fuel utilization. Beyond this point, entropy rises, reflecting system degradation and lower energy efficiency. The results show that entropy analysis can provide valuable insights into fuel behavior and operational limits. The proposed scaling method may also serve to control a Monte Carlo simulation, especially for the analysis of long-life reactors. Full article
(This article belongs to the Special Issue Insight into Entropy)
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