Shannon entropy is currently the most popular method for quantifying the disorder or information of a spatial data set such as a landscape pattern and a cartographic map. However, its drawback when applied to spatial data is also well documented; it is incapable of capturing configurational disorder. In addition, it has been recently criticized to be thermodynamically irrelevant. Therefore, Boltzmann entropy was revisited, and methods have been developed for its calculation with landscape patterns. The latest method was developed based on the Wasserstein metric. This method incorporates spatial repetitiveness, leading to a Wasserstein metric-based Boltzmann entropy that is capable of capturing the configurational disorder of a landscape mosaic. However, the numerical work required to calculate this entropy is beyond what can be practically achieved through hand calculation. This study developed a new software tool for conveniently calculating the Wasserstein metric-based Boltzmann entropy. The tool provides a user-friendly human-computer interface and many functions. These functions include multi-format data file import function, calculation function, and data clear or copy function. This study outlines several essential technical implementations of the tool and reports the evaluation of the software tool and a case study. Experimental results demonstrate that the software tool is both efficient and convenient.
Download full-text PDF |
Source |
|---|---|
| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7516855 | PMC |
| http://dx.doi.org/10.3390/e22040381 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
Applications of Entropy in Data Analysis and Machine Learning: A Review.
Entropy (Basel)
December 2024
Centro de Investigación Operativa, Universidad Miguel Hernández de Elche, 03202 Elche, Spain.
Since its origin in the thermodynamics of the 19th century, the concept of entropy has also permeated other fields of physics and mathematics, such as Classical and Quantum Statistical Mechanics, Information Theory, Probability Theory, Ergodic Theory and the Theory of Dynamical Systems. Specifically, we are referring to the classical entropies: the Boltzmann-Gibbs, von Neumann, Shannon, Kolmogorov-Sinai and topological entropies. In addition to their common name, which is historically justified (as we briefly describe in this review), another commonality of the classical entropies is the important role that they have played and are still playing in the theory and applications of their respective fields and beyond.
View Article and Find Full Text PDFRevisions of the Phenomenological and Statistical Statements of the Second Law of Thermodynamics.
Entropy (Basel)
December 2024
Istituto Nazionale di Alta Matematica (INdAM), 00185 Rome, Italy.
The status of the Second Law of Thermodynamics, even in the 21st century, is not as certain as when Arthur Eddington wrote about it a hundred years ago. It is not only about the truth of this law, but rather about its strict and exhaustive formulation. In the previous article, it was shown that two of the three most famous thermodynamic formulations of the Second Law of Thermodynamics are non-exhaustive.
View Article and Find Full Text PDFThe Boltzmann Equation and Its Place in the Edifice of Statistical Mechanics.
Entropy (Basel)
December 2024
Department of Philosophy, Logic and Scientific Method, London School of Economics, Houghton Street, London WC2A 2AE, UK.
It is customary to classify approaches in statistical mechanics (SM) as belonging either to Boltzmanninan SM (BSM) or Gibbsian SM (GSM). It is, however, unclear how the Boltzmann equation (BE) fits into either of these approaches. To discuss the relation between BE and BSM, we first present a version of BSM that differs from standard presentation in that it uses local field variables to individuate macro-states, and we then show that BE is a special case of BSM .
View Article and Find Full Text PDFCascades Towards Noise-Induced Transitions on Networks Revealed Using Information Flows.
Entropy (Basel)
December 2024
Institute of Informatics, University of Amsterdam, 1098 XH Amsterdam, The Netherlands.
Complex networks, from neuronal assemblies to social systems, can exhibit abrupt, system-wide transitions without external forcing. These endogenously generated "noise-induced transitions" emerge from the intricate interplay between network structure and local dynamics, yet their underlying mechanisms remain elusive. Our study unveils two critical roles that nodes play in catalyzing these transitions within dynamical networks governed by the Boltzmann-Gibbs distribution.
View Article and Find Full Text PDFThe Thermodynamics of the Van Der Waals Black Hole Within Kaniadakis Entropy.
Entropy (Basel)
November 2024
Institute of Fundamental and Applied Research, National Research University TIIAME, Kori Niyoziy 39, Tashkent 100000, Uzbekistan.
In this work, we have studied the thermodynamic properties of the Van der Waals black hole in the framework of the relativistic Kaniadakis entropy. We have shown that the black hole properties, such as the mass and temperature, differ from those obtained by using the the Boltzmann-Gibbs approach. Moreover, the deformation κ-parameter changes the behavior of the Gibbs free energy via introduced thermodynamic instabilities, whereas the emission rate is influenced by κ only at low frequencies.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!