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Entropy
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Applications of Fisher Information in Sciences II
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Applications of Fisher Information in Sciences II

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

Deadline for manuscript submissions: 21 March 2025 | Viewed by 8421

Special Issue Editor

Dr. Takuya Yamano

E-Mail Website
Guest Editor
Department of Mathematics and Physics, Faculty of Science, Kanagawa University, 3-27-1 Rokkakubashi, Yokohama 221-8686, Kanagawa, Japan
Interests: fisher information; non-extensivity; information theory; nonlinear Fokker–Planck equations; non-linear Schrödinger equations; complexity measure; irreversibility; tumor growth; temperature-dependent energy levels in statistical physics
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Special Issue Information

Dear Colleagues,

This Special Issue aims to present a collection of articles addressing recent research that delves into various aspects of Fisher information and its applications. Since we launched the first edition of this Special Issue in  2016 (https://www.mdpi.com/journal/entropy/special_issues/fisher_information_in_sciences),  this information measure has attracted increasing interest, and ongoing insights into its applications have been accumulated in various fields.

It is well recognized that Ronald A. Fisher originally presented this information in his statistical estimation theory a century ago (Philos. Trans. Roy. Soc., London, Sec. A, 222 (1922) 309-368), and that it has offered an indispensable tool with which to analyze statistical systems. To date, it has also received extensive attention from researchers working in fields beyond statistics. Statistical physics, thermodynamics, and quantum science are, indeed, intimately associated with this measure. In addition, astronomy and biological sciences reap most of the benefits of this tool for big data analysis. The applications of Fisher information are in fact vast, and have played expanding roles in the advancement of each discipline. For example, precise temperature measurement and its development are becoming crucial tasks in modern quantum technologies and the advancement of thermodynamics in the quantum region.

In this renewed Special Issue, we would like to compile articles addressing the fundamental aspects of Fisher information and its applications in various fields. We welcome submissions that shed new light on the scope of this information’s in-depth features and unreported useful applications. The intended topics are listed in the keywords below, but the contributors may address them in a broader sense.

Dr. Takuya Yamano
Guest Editor

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

  • fisher information
  • relative fisher information (Hyvärinen divergence)
  • fisher information matrix
  • quantum metrology
  • quantum Fisher information
  • skew information
  • statistical estimation theory
  • de Bruijn’s identity
  • Cramer–Rao bound
  • Jeffreys prior
  • quantum multiparameter estimation
  • curvature of the statistical model
  • quantum measurement
  • quantum thermometry
  • quantum thermodynamics
  • gradient flow
  • logarithmic Sobolev inequality
  • phase space gradient
  • Jensen–Fisher divergence
  • information geometry
  • Fisher–Rao metric
  • complexity
  • data analysis
  • gravitational wave
  • cosmological information

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Published Papers (3 papers)

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Research

9 pages, 238 KiB  
Article
Dirac Equation and Fisher Information
by Asher Yahalom
Entropy 2024, 26(11), 971; https://doi.org/10.3390/e26110971 - 12 Nov 2024
Viewed by 594
Abstract
Previously, it was shown that Schrödinger’s theory can be derived from a potential flow Lagrangian provided a Fisher information term is added. This approach was later expanded to Pauli’s theory of an electron with spin, which required a Clebsch flow Lagrangian with non-zero [...] Read more.
Previously, it was shown that Schrödinger’s theory can be derived from a potential flow Lagrangian provided a Fisher information term is added. This approach was later expanded to Pauli’s theory of an electron with spin, which required a Clebsch flow Lagrangian with non-zero vorticity. Here, we use the recent relativistic flow Lagrangian to represent Dirac’s theory with the addition of a Lorentz invariant Fisher information term as is required by quantum mechanics. Full article
(This article belongs to the Special Issue Applications of Fisher Information in Sciences II)
73 pages, 6672 KiB  
Article
Exploring Limit Cycles of Differential Equations through Information Geometry Unveils the Solution to Hilbert’s 16th Problem
by Vinícius Barros da Silva, João Peres Vieira and Edson Denis Leonel
Entropy 2024, 26(9), 745; https://doi.org/10.3390/e26090745 - 30 Aug 2024
Viewed by 5454
Abstract
The detection of limit cycles of differential equations poses a challenge due to the type of the nonlinear system, the regime of interest, and the broader context of applicable models. Consequently, attempts to solve Hilbert’s sixteenth problem on the maximum number of limit [...] Read more.
The detection of limit cycles of differential equations poses a challenge due to the type of the nonlinear system, the regime of interest, and the broader context of applicable models. Consequently, attempts to solve Hilbert’s sixteenth problem on the maximum number of limit cycles of polynomial differential equations have been uniformly unsuccessful due to failing results and their lack of consistency. Here, the answer to this problem is finally obtained through information geometry, in which the Riemannian metrical structure of the parameter space of differential equations is investigated with the aid of the Fisher information metric and its scalar curvature R. We find that the total number of divergences of |R| to infinity provides the maximum number of limit cycles of differential equations. Additionally, we demonstrate that real polynomial systems of degree n≥2 have the maximum number of 2(n−1)(4(n−1)−2) limit cycles. The research findings highlight the effectiveness of geometric methods in analyzing complex systems and offer valuable insights across information theory, applied mathematics, and nonlinear dynamics. These insights may pave the way for advancements in differential equations, presenting exciting opportunities for future developments. Full article
(This article belongs to the Special Issue Applications of Fisher Information in Sciences II)
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33 pages, 431 KiB  
Article
The Inverse of Exact Renormalization Group Flows as Statistical Inference
by David S. Berman and Marc S. Klinger
Entropy 2024, 26(5), 389; https://doi.org/10.3390/e26050389 - 30 Apr 2024
Cited by 13 | Viewed by 1558
Abstract
We build on the view of the Exact Renormalization Group (ERG) as an instantiation of Optimal Transport described by a functional convection–diffusion equation. We provide a new information-theoretic perspective for understanding the ERG through the intermediary of Bayesian Statistical Inference. This connection is [...] Read more.
We build on the view of the Exact Renormalization Group (ERG) as an instantiation of Optimal Transport described by a functional convection–diffusion equation. We provide a new information-theoretic perspective for understanding the ERG through the intermediary of Bayesian Statistical Inference. This connection is facilitated by the Dynamical Bayesian Inference scheme, which encodes Bayesian inference in the form of a one-parameter family of probability distributions solving an integro-differential equation derived from Bayes’ law. In this note, we demonstrate how the Dynamical Bayesian Inference equation is, itself, equivalent to a diffusion equation, which we dub Bayesian Diffusion. By identifying the features that define Bayesian Diffusion and mapping them onto the features that define the ERG, we obtain a dictionary outlining how renormalization can be understood as the inverse of statistical inference. Full article
(This article belongs to the Special Issue Applications of Fisher Information in Sciences II)
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