The form invariance of pseudoadditivity is shown to determine the structure of nonextensive entropies. Nonextensive entropy is defined as the appropriate expectation value of nonextensive information content, similar to the definition of Shannon entropy. Information content in a nonextensive system is obtained uniquely from generalized axioms by replacing the usual additivity with pseudoadditivity. The satisfaction of the form invariance of the pseudoadditivity of nonextensive entropy and its information content is found to require the normalization of nonextensive entropies. The proposed principle requires the same normalization as that derived previously [A.K. Rajagopal and S. Abe, Phys. Rev. Lett. 83, 1711 (1999)], but is simpler and establishes a basis for the systematic definition of various entropies in nonextensive systems.
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Entropy (Basel)
November 2024
Laboratory of Parallel Architectures for Signal Processing, Universidade Federal do Rio Grande do Norte, Natal 59078-900, RN, Brazil.
We investigate multimodal seismicity by analyzing it as the result of multiple seismic sources. We examine three case studies: the Redoubt and Spurr regions in Alaska, where volcanic and subduction-related seismicity occur, and the Kii Peninsula in Japan, where shallow and deep earthquakes are clearly separated. To understand this phenomenon, we perform spatial, temporal, and magnitude analyses.
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September 2024
Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland.
We present a comparative analysis of the plethora of nonextensive and/or nonadditive entropies which go beyond the standard Boltzmann-Gibbs formulation. After defining the basic notions of additivity, extensivity, and composability, we discuss the properties of these entropies and their mutual relations, if they exist. The results are presented in two informative tables that are of strong interest to the gravity and cosmology community in the context of the recently intensively explored horizon entropies for black hole and cosmological models.
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September 2024
Department of Astrophysical Sciences, Princeton University, Princeton, NJ, 08544, USA.
We introduce the theory of thermodynamic relativity, a unified theoretical framework for describing both entropies and velocities, and their respective physical disciplines of thermodynamics and kinematics, which share a surprisingly identical description with relativity. This is the first study to generalize relativity in a thermodynamic context, leading naturally to anisotropic and nonlinear adaptations of relativity; thermodynamic relativity constitutes a new path of generalization, as compared to the "traditional" passage from special to general theory based on curved spacetime. We show that entropy and velocity are characterized by three identical postulates, which provide the basis of a broader framework of relativity: (1) no privileged reference frame with zero value; (2) existence of an invariant and fixed value for all reference frames; and (3) existence of stationarity.
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September 2024
College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China.
Tsallis entropy has been widely used in image thresholding because of its non-extensive properties. The non-extensive parameter contained in this entropy plays an important role in various adaptive algorithms and has been successfully applied in bi-level image thresholding. In this paper, the relationships between parameter and pixels' long-range correlations have been further studied within multi-threshold image segmentation.
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June 2024
Department of Physics, Faculty of Arts and Sciences, Izmir University of Economics, Izmir 35330, Turkey.
Almost two decades ago, Ernesto P. Borges and Bruce M. Boghosian embarked on the intricate task of composing a manuscript to honor the profound contributions of Constantino Tsallis to the realm of statistical physics, coupled with a concise exploration of -Statistics.
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