Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
4.7
2.7
Journals
Entropy
Special Issues
The Statistical Foundations of Entropy II
entropy-logo
Submit to Entropy Review for Entropy Propose a Special Issue

Journal Menu

► Journal Menu

Journal Browser

► Journal Browser
share announcement

The Statistical Foundations of Entropy II

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

Deadline for manuscript submissions: closed (14 September 2023) | Viewed by 4844

Special Issue Editors

Dr. Petr Jizba

E-Mail Website
Guest Editor
Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Břehová 7, 115 19 Prague, Czech Republic
Interests: non-equilibrium thermodynamics; stochastic processes; superstatistics; econophysics; transfer entropies; generalized entropies; Feynman’s path integral; quantum theory; critical phenomena
Special Issues, Collections and Topics in MDPI journals
Dr. Jan Korbel

E-Mail Website
Guest Editor
Department of Science for Complex Systems, Medical University of Vienna & CSH Associate Faculty, 1080 Vienna, Austria
Interests: complex systems; econophysics; stochastic thermodynamics; theory of information; networks; generalized entropies
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

During the last two decades, the understanding of complex dynamical systems underwent important conceptual shifts. The catalyst has been the infusion of new ideas from the theory of critical phenomena (scaling laws, renormalization group, etc.), (multi)fractals and trees, random matrix theory, network theory, and non-Shannonian information theory. On the other hand, the usual Boltzmann–Gibbs statistics has proven to be grossly inadequate in this context. While successful in describing stationary systems characterized by ergodicity or metric transitivity, Boltzmann–Gibbs statistics fail to reproduce the complex statistical behavior of many real-world systems in biology, astrophysics, geology, and the economic and social sciences.

Following the success of the first Special Issue, we continue this Special Issue as a second volume in order to encourage researchers to present an original piece of work that could contribute to an ongoing discussion on the statistical foundations of entropy, with a particular emphasis on entropies describing complex systems that cannot be described within the established framework.

Expected contributions should address, on the one-hand, purely conceptual issues ranging from non-equilibrium statistical physics and (quantum) thermodynamics to information and estimation theory, and on the other hand, they should be related to applications (e.g., in complex dynamical systems, network structures, classical and quantum coding theory or stochastic thermodynamics).

A particular focus of this Special Issue is to establish a connection between the two key entropy concepts, namely thermodynamic entropy and information-theoretic theory, with complex systems serving as a springboard for a deeper discussion and analysis of this issue. Particularly issues such as the connection between entropy production and information production in complex systems or generalized coding theorems and the identification of ensuing generalized information entropies in terms of data compression limits are expected to be addressed in greater depth.

To see the first volume of The Statistical Foundations of Entropy, please click it at:

https://www.mdpi.com/journal/entropy/special_issues/Statistical_Foundations

Dr. Petr Jizba
Dr. Jan Korbel
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

  • generalized entropies
  • non-equilibrium processes
  • generalizations of statistical mechanics
  • complex systems
  • quantum systems
  • information-theoretic entropies
  • axiomatic approaches

Published Papers (3 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

Jump to: Other

21 pages, 501 KiB  
Article
Constraints on Tsallis Cosmology from Big Bang Nucleosynthesis and the Relic Abundance of Cold Dark Matter Particles
by Petr Jizba and Gaetano Lambiase
Entropy 2023, 25(11), 1495; https://doi.org/10.3390/e25111495 - 29 Oct 2023
Cited by 2 | Viewed by 1061
Abstract
By employing Tsallis’ extensive but non-additive δ-entropy, we formulate the first two laws of thermodynamics for gravitating systems. By invoking Carathéodory’s principle, we pay particular attention to the integrating factor for the heat one-form. We show that the latter factorizes into the [...] Read more.
By employing Tsallis’ extensive but non-additive δ-entropy, we formulate the first two laws of thermodynamics for gravitating systems. By invoking Carathéodory’s principle, we pay particular attention to the integrating factor for the heat one-form. We show that the latter factorizes into the product of thermal and entropic parts, where the entropic part cannot be reduced to a constant, as is the case in conventional thermodynamics, due to the non-additive nature of Sδ. The ensuing two laws of thermodynamics imply a Tsallis cosmology, which is then applied to a radiation-dominated universe to address the Big Bang nucleosynthesis and the relic abundance of cold dark matter particles. It is demonstrated that the Tsallis cosmology with the scaling exponent δ∼1.499 (or equivalently, the anomalous dimension Δ∼0.0013) consistently describes both the abundance of cold dark matter particles and the formation of primordial light elements, such as deuterium 2H and helium 4He. Salient issues, including the zeroth law of thermodynamics for the δ-entropy and the lithium 7Li problem, are also briefly discussed. Full article
(This article belongs to the Special Issue The Statistical Foundations of Entropy II)
►▼ Show Figures

Figure 1

23 pages, 2911 KiB  
Article
The Typical Set and Entropy in Stochastic Systems with Arbitrary Phase Space Growth
by Rudolf Hanel and Bernat Corominas-Murtra
Entropy 2023, 25(2), 350; https://doi.org/10.3390/e25020350 - 14 Feb 2023
Viewed by 1399
Abstract
The existence of the typical set is key for data compression strategies and for the emergence of robust statistical observables in macroscopic physical systems. Standard approaches derive its existence from a restricted set of dynamical constraints. However, given its central role underlying the [...] Read more.
The existence of the typical set is key for data compression strategies and for the emergence of robust statistical observables in macroscopic physical systems. Standard approaches derive its existence from a restricted set of dynamical constraints. However, given its central role underlying the emergence of stable, almost deterministic statistical patterns, a question arises whether typical sets exist in much more general scenarios. We demonstrate here that the typical set can be defined and characterized from general forms of entropy for a much wider class of stochastic processes than was previously thought. This includes processes showing arbitrary path dependence, long range correlations or dynamic sampling spaces, suggesting that typicality is a generic property of stochastic processes, regardless of their complexity. We argue that the potential emergence of robust properties in complex stochastic systems provided by the existence of typical sets has special relevance to biological systems. Full article
(This article belongs to the Special Issue The Statistical Foundations of Entropy II)
►▼ Show Figures

Figure 1

Other

Jump to: Research

17 pages, 464 KiB  
Opinion
Senses along Which the Entropy Sq Is Unique
by Constantino Tsallis
Entropy 2023, 25(5), 743; https://doi.org/10.3390/e25050743 - 01 May 2023
Cited by 6 | Viewed by 1533
Abstract
The Boltzmann–Gibbs–von Neumann–Shannon additive entropy SBG=−k∑ipilnpi as well as its continuous and quantum counterparts, constitute the grounding concept on which the BG statistical mechanics is constructed. This magnificent theory has produced, [...] Read more.
The Boltzmann–Gibbs–von Neumann–Shannon additive entropy SBG=−k∑ipilnpi as well as its continuous and quantum counterparts, constitute the grounding concept on which the BG statistical mechanics is constructed. This magnificent theory has produced, and will most probably keep producing in the future, successes in vast classes of classical and quantum systems. However, recent decades have seen a proliferation of natural, artificial and social complex systems which defy its bases and make it inapplicable. This paradigmatic theory has been generalized in 1988 into the nonextensive statistical mechanics—as currently referred to—grounded on the nonadditive entropy Sq=k1−∑ipiqq−1 as well as its corresponding continuous and quantum counterparts. In the literature, there exist nowadays over fifty mathematically well defined entropic functionals. Sq plays a special role among them. Indeed, it constitutes the pillar of a great variety of theoretical, experimental, observational and computational validations in the area of complexity—plectics, as Murray Gell-Mann used to call it. Then, a question emerges naturally, namely In what senses is entropy Sq unique? The present effort is dedicated to a—surely non exhaustive—mathematical answer to this basic question. Full article
(This article belongs to the Special Issue The Statistical Foundations of Entropy II)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-3
Back to TopTop