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Entropic Forms and Related Algebras
Istituto Sistemi Complessi (ISC–CNR) c/o Dipartimento di Scienza Applicata e Tecnologia-Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino, I-10129, Italy
Received: 16 November 2012; in revised form: 16 January 2013 / Accepted: 30 January 2013 / Published: 7 February 2013
Abstract: Starting from a very general trace-form entropy, we introduce a pair of algebraic structures endowed by a generalized sum and a generalized product. These algebras form, respectively, two Abelian fields in the realm of the complex numbers isomorphic each other. We specify our results to several entropic forms related to distributions recurrently observed in social, economical, biological and physical systems including the stretched exponential, the power-law and the interpolating Bosons-Fermions distributions. Some potential applications in the study of complex systems are advanced.
Keywords: entropies; algebraic structures; power-law distributions; stretched exponential; interpolating Bosons-Fermions distributions
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MDPI and ACS Style
Scarfone, A.M. Entropic Forms and Related Algebras. Entropy 2013, 15, 624-649.
Scarfone AM. Entropic Forms and Related Algebras. Entropy. 2013; 15(2):624-649.
Scarfone, Antonio M. 2013. "Entropic Forms and Related Algebras." Entropy 15, no. 2: 624-649.