Authors: Ilić, Velimir 
Scarfone, Antonio Maria
Wada, Tatsuaki
Title: Equivalence between four versions of thermostatistics based on strongly pseudoadditive entropies
Journal: Physical Review E
Volume: 100
Issue: 6
Issue Date: 26-Dec-2019
Rank: M21
ISSN: 2470-0045
DOI: 10.1103/PhysRevE.100.062135
The class of strongly pseudoadditive (SPA) entropies, which can be represented as an increasing continuous transformation of Shannon and Rényi entropies, have intensively been studied in previous decades. Although their mathematical structure has thoroughly been explored and established by generalized Shannon-Khinchin axioms, the analysis of their thermostatistical properties have mostly been limited to special cases which belong to two parameter Sharma-Mittal entropy class, such as Tsallis, Renyi and Gaussian entropies. In this paper we present a general analysis of the strongly pseudoadditive entropies thermostatistics by taking into account both linear and escort constraints on internal energy. We develop two types of dualities between the thermostatistics formalisms. By the first one, the formalism of Rényi entropy is transformed in the formalism of SPA entropy under general energy constraint and, by the second one, the generalized thermostatistics which corresponds to the linear constraint is transformed into the one which corresponds to the escort constraint. Thus, we establish the equivalence between four different thermostatistics formalisms based on Rényi and SPA entropies coupled with linear and escort constraints and we provide the transformation formulas. In this way we obtain a general framework which is applicable to the wide class of entropies and constraints previously discussed in the literature. As an example, we rederive maximum entropy distributions for Sharma-Mittal entropy and we establish new relationships between the corresponding thermodynamic potentials. We obtain, as special cases, previously developed expressions for maximum entropy distributions and thermodynamic quantities for Tsallis, Rényi, and Gaussian entropies. In addition, the results are applied for derivation of thermostatistical relationships for supraextensive entropy, which has not previously been considered.
Publisher: American Physical Society
Project: Development of new information and communication technologies, based on advanced mathematical methods, with applications in medicine, telecommunications, power systems, protection of national heritage and education 
Representations of logical structures and formal languages and their application in computing 
Japan Society for the Promotion of Science (JSPS) Grants-in-Aid for Scientific Research (KAKENHI), Grant No. JP17K05341

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