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Entropy 2013, 15(2), 624-649; doi:10.3390/e15020624
Article

Entropic Forms and Related Algebras

Received: 16 November 2012 / Revised: 16 January 2013 / Accepted: 30 January 2013 / Published: 7 February 2013
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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 entropies; algebraic structures; power-law distributions; stretched exponential; interpolating Bosons-Fermions distributions
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Scarfone, A.M. Entropic Forms and Related Algebras. Entropy 2013, 15, 624-649.

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