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Entropy
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Concepts of Entropy and Their Applications III
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Concepts of Entropy and Their Applications III

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

Deadline for manuscript submissions: closed (29 February 2024) | Viewed by 10626

Special Issue Editor

Prof. Dr. Philip Broadbridge

E-Mail Website
Guest Editor
Department of Mathematics and Statistics, 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

Special Issue Information

Dear Colleagues,

There are alternative definitions of entropy that largely reflect different scientific perspectives of classical thermodynamics, materials science, statistical mechanics, classical and quantum information theory, as well as ergodic and chaotic dynamical systems. Since the first and second rounds of this Special Issue, there have been several generalisations of the traditional definitions of thermodynamic entropy and Shannon information-related entropy. Such generalisations should not be made for the sake of abstraction; they need to demonstrate utility in better understanding real phenomena in physics, chemistry, biology, psychology and information technology. Increasing entropy has been an indicator of irreversibility, Clausius’ “disgregation”, disorder and information loss. Which state functions and analytic tools can best clarify these phenomena, and how are these various tools related mathematically, conceptually and practically? This Special Issue welcomes significant contributions that help to answer these questions.

Prof. Dr. Philip Broadbridge
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

  • mathematics of entropy
  • inter-related concepts
  • irreversibility in real systems

Related Special Issues

Published Papers (7 papers)

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Research

11 pages, 266 KiB  
Article
Convergence of Relative Entropy for Euler–Maruyama Scheme to Stochastic Differential Equations with Additive Noise
by Yuan Yu
Entropy 2024, 26(3), 232; https://doi.org/10.3390/e26030232 - 06 Mar 2024
Viewed by 737
Abstract
For a family of stochastic differential equations driven by additive Gaussian noise, we study the asymptotic behaviors of its corresponding Euler–Maruyama scheme by deriving its convergence rate in terms of relative entropy. Our results for the convergence rate in terms of relative entropy [...] Read more.
For a family of stochastic differential equations driven by additive Gaussian noise, we study the asymptotic behaviors of its corresponding Euler–Maruyama scheme by deriving its convergence rate in terms of relative entropy. Our results for the convergence rate in terms of relative entropy complement the conventional ones in the strong and weak sense and induce some other properties of the Euler–Maruyama scheme. For example, the convergence in terms of the total variation distance can be implied by Pinsker’s inequality directly. Moreover, when the drift is β(0<β<1)-Hölder continuous in the spatial variable, the convergence rate in terms of the weighted variation distance is also established. Both of these convergence results do not seem to be directly obtained from any other convergence results of the Euler–Maruyama scheme. The main tool this paper relies on is the Girsanov transform. Full article
(This article belongs to the Special Issue Concepts of Entropy and Their Applications III)
19 pages, 14960 KiB  
Article
Numerical Study on Local Entropy Production Mechanism of a Contra-Rotating Fan
by Xingyu Jia and Xi Zhang
Entropy 2023, 25(9), 1293; https://doi.org/10.3390/e25091293 - 03 Sep 2023
Viewed by 1137
Abstract
Contra-rotating fans (CRFs) have garnered significant attention due to their higher power-to-weight ratio compared to traditional fans; however, limited focus has been given to the localization and development of local aerodynamic losses. Furthermore, there is a need for further research on the impact [...] Read more.
Contra-rotating fans (CRFs) have garnered significant attention due to their higher power-to-weight ratio compared to traditional fans; however, limited focus has been given to the localization and development of local aerodynamic losses. Furthermore, there is a need for further research on the impact of load distribution along the radius on local entropy production. Therefore, this study aims to investigate a contra-rotating fan as the research subject. An optimal design for load distribution along the radius is achieved by constructing a surrogate model in combination with a genetic algorithm. The effectiveness of this design has been verified through experimentation using a specific test device. In this study, a local entropy production rate (EPR) model adapted to the shear stress transport-detached eddy simulation (SST-DES) technique is constructed to evaluate the loss distribution of the contra-rotating fan. This paper primarily focuses on comparing and analyzing the blade profile and overall performance of the CRFs before and after optimization. The EPR contribution of each interval along the radius is compared to the corresponding blade channel to identify the approximate range of high-EPR regions. Furthermore, an investigation is conducted to examine the distribution of EPR along the streamwise direction in these high-EPR regions. After that, by comparing the development of the flow structure near a stall before and after optimization, combined with the analysis of the EPR contours, the EPR mechanism of this CRF is revealed. Full article
(This article belongs to the Special Issue Concepts of Entropy and Their Applications III)
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16 pages, 6663 KiB  
Article
TMD Design by an Entropy Index for Seismic Control of Tall Shear-Bending Buildings
by Yumei Wang and Zhe Qu
Entropy 2023, 25(8), 1110; https://doi.org/10.3390/e25081110 - 25 Jul 2023
Viewed by 736
Abstract
This study proposes a new arrangement-tuning method to maximize the potential of tuned mass dampers (TMDs) in decreasing the seismic responses of tall buildings. The method relies on a Grammian-based entropy index with the physical meaning of covariance responses to white noise without [...] Read more.
This study proposes a new arrangement-tuning method to maximize the potential of tuned mass dampers (TMDs) in decreasing the seismic responses of tall buildings. The method relies on a Grammian-based entropy index with the physical meaning of covariance responses to white noise without the involvement of external inputs. A twelve-story RC frame-shear wall building was used as an example to illustrate the method. Indices were computed for the building with TMDs placed on different stories and tuning to different modes and were compared with responses to white noise (colored) time histories. Results showed that greater index reduction cases agree well with greater story-drift reductions cases, despite the differences in the time step of the white noises and structural model types (pure shear vs. shear-bending), and the optimal TMD is not necessarily the traditional “roof—1st mode tuning” case. Comparisons were also made for the shear-bending building under seven earthquake excitations. It is found that, though TMDs are not full-band effective controllers, the index-selected TMDs still perform the best in three out of seven earthquakes. So, the proposed internal-property-based entropy index provides a good controller design for large-scale structures under unpredictable none-stationary excitations. Full article
(This article belongs to the Special Issue Concepts of Entropy and Their Applications III)
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14 pages, 774 KiB  
Article
An Entropic Approach for Pair Trading in PSX
by Laiba Amer and Tanweer Ul Islam
Entropy 2023, 25(3), 494; https://doi.org/10.3390/e25030494 - 13 Mar 2023
Viewed by 1248
Abstract
The perception in pair trading is to recognize that when two stocks move together, their prices will converge to a mean value in the future. However, finding the mean-reverted point at which the value of the pair will converge as well as the [...] Read more.
The perception in pair trading is to recognize that when two stocks move together, their prices will converge to a mean value in the future. However, finding the mean-reverted point at which the value of the pair will converge as well as the optimal boundaries of the trade is not easy, as uncertainty and model misspecifications may lead to losses. To cater to these problems, this study employed a novel entropic approach that utilizes entropy as a penalty function for the misspecification of the model. The use of entropy as a measure of risk in pair trading is a nascent idea, and this study utilized daily data for 64 companies listed on the PSX for the years 2017, 2018, and 2019 to compute their returns based on the entropic approach. The returns to these stocks were then evaluated and compared with the buy and hold strategy. The results show positive and significant returns from pair trading using an entropic approach. The entropic approach seems to have an edge to buy and hold, distance-based, and machine learning approaches in the context of the Pakistani market. Full article
(This article belongs to the Special Issue Concepts of Entropy and Their Applications III)
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21 pages, 3195 KiB  
Article
Entropy as a Measure of Consistency in Software Architecture
by Stanislaw Jerzy Niepostyn and Wiktor Bohdan Daszczuk
Entropy 2023, 25(2), 328; https://doi.org/10.3390/e25020328 - 10 Feb 2023
Cited by 1 | Viewed by 1523
Abstract
In building software architectures, the relations between elements in different diagrams are often overlooked. The first stage of building IT systems is the use of ontology terminology, not software terminology, in the requirements engineering process. Then, when constructing software architecture, IT architects more [...] Read more.
In building software architectures, the relations between elements in different diagrams are often overlooked. The first stage of building IT systems is the use of ontology terminology, not software terminology, in the requirements engineering process. Then, when constructing software architecture, IT architects more or less consciously however introduce elements that represent the same classifier on different diagrams with similar names. These connections are called consistency rules and are usually not attached in any way in a modeling tool, and only a significant number of them in the models increase the quality of the software architecture. It is mathematically proved that the application of consistency rules increases the information content of software architecture. Authors show that increasing readability and ordering of software architecture by means of consistency rules have their mathematical rationale. In this article, we found proof of decreasing Shannon entropy while applying consistency rules in the construction of software architecture of IT systems. Therefore, it has been shown that marking selected elements in different diagrams with these same names is, therefore, an implicit way to increase the information content of software architecture while simultaneously improving its orderliness and readability. Moreover, this increase in the quality of the software architecture can be measured by entropy, which allows for checking whether the number of consistency rules is sufficient to compare different architectures, even of different sizes, thanks to entropy normalization, and checking during the development of the software architecture, what is the improvement in its orderliness and readability. Full article
(This article belongs to the Special Issue Concepts of Entropy and Their Applications III)
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37 pages, 2099 KiB  
Article
Covariant Lyapunov Vectors and Finite-Time Normal Modes for Geophysical Fluid Dynamical Systems
by Jorgen S. Frederiksen
Entropy 2023, 25(2), 244; https://doi.org/10.3390/e25020244 - 29 Jan 2023
Viewed by 979
Abstract
Dynamical vectors characterizing instability and applicable as ensemble perturbations for prediction with geophysical fluid dynamical models are analysed. The relationships between covariant Lyapunov vectors (CLVs), orthonormal Lyapunov vectors (OLVs), singular vectors (SVs), Floquet vectors and finite-time normal modes (FTNMs) are examined for periodic [...] Read more.
Dynamical vectors characterizing instability and applicable as ensemble perturbations for prediction with geophysical fluid dynamical models are analysed. The relationships between covariant Lyapunov vectors (CLVs), orthonormal Lyapunov vectors (OLVs), singular vectors (SVs), Floquet vectors and finite-time normal modes (FTNMs) are examined for periodic and aperiodic systems. In the phase-space of FTNM coefficients, SVs are shown to equate with unit norm FTNMs at critical times. In the long-time limit, when SVs approach OLVs, the Oseledec theorem and the relationships between OLVs and CLVs are used to connect CLVs to FTNMs in this phase-space. The covariant properties of both the CLVs, and the FTNMs, together with their phase-space independence, and the norm independence of global Lyapunov exponents and FTNM growth rates, are used to establish their asymptotic convergence. Conditions on the dynamical systems for the validity of these results, particularly ergodicity, boundedness and non-singular FTNM characteristic matrix and propagator, are documented. The findings are deduced for systems with nondegenerate OLVs, and, as well, with degenerate Lyapunov spectrum as is the rule in the presence of waves such as Rossby waves. Efficient numerical methods for the calculation of leading CLVs are proposed. Norm independent finite-time versions of the Kolmogorov-Sinai entropy production and Kaplan-Yorke dimension are presented. Full article
(This article belongs to the Special Issue Concepts of Entropy and Their Applications III)
11 pages, 1415 KiB  
Article
Decoding ‘Maximum Entropy’ Deconvolution
by Long V. Le, Tae Jung Kim, Young Dong Kim and David E. Aspnes
Entropy 2022, 24(9), 1238; https://doi.org/10.3390/e24091238 - 02 Sep 2022
Cited by 2 | Viewed by 3227
Abstract
For over five decades, the mathematical procedure termed “maximum entropy” (M-E) has been used to deconvolve structure in spectra, optical and otherwise, although quantitative measures of performance remain unknown. Here, we examine this procedure analytically for the lowest two orders for a Lorentzian [...] Read more.
For over five decades, the mathematical procedure termed “maximum entropy” (M-E) has been used to deconvolve structure in spectra, optical and otherwise, although quantitative measures of performance remain unknown. Here, we examine this procedure analytically for the lowest two orders for a Lorentzian feature, obtaining expressions for the amount of sharpening and identifying how spurious structures appear. Illustrative examples are provided. These results enhance the utility of this widely used deconvolution approach to spectral analysis. Full article
(This article belongs to the Special Issue Concepts of Entropy and Their Applications III)
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