RT Journal Article
T1 Beyond the Shannon-Khinchin formulation: The composability axiom and the universal-group entropy.
A1 Tempesta, Piergiulio
AB The notion of entropy is ubiquitous both in natural and social sciences. In the last two decades, a considerable effort has been devoted to the study of new entropic forms, which generalize the standard Boltzmann-Gibbs (BC) entropy and could be applicable in thermodynamics, quantum mechanics and information theory. In Khinchin (1957), by extending previous ideas of Shannon (1948) and Shannon and Weaver (1949), Khinchin proposed a characterization of the BG entropy, based on four requirements, nowadays known as the Shannon-Khinchin (SK) axioms. The purpose of this paper is twofold. First, we show that there exists an intrinsic group-theoretical structure behind the notion of entropy. It comes from the requirement of composability of an entropy with respect to the union of two statistically independent systems, that we propose in an axiomatic formulation. Second, we show that there exists a simple universal family of trace form entropies. This class contains many well known examples of entropies and infinitely many new ones, a priori multi-parametric. Due to its specific relation with Lazard's universal formal group of algebraic topology, the new general entropy introduced in this work will be called the universal-group entropy. A new example of multi-parametric entropy is explicitly constructed.
PB Elsevier Masson
SN 0003-4916
YR 2016
FD 2016-02
LK https://hdl.handle.net/20.500.14352/24420
UL https://hdl.handle.net/20.500.14352/24420
LA eng
NO © 2015 Elsevier Inc.I wish to thank heartily prof. C. Tsallis for a careful reading of the manuscript and many useful discussions, and prof. G. Parisi for reading the manuscript and for encouragement. Interesting discussions with prof. A. González López, F. Finkel, R.A. Leo, M.A. Rodríguez and G. Sicuro are also gratefully acknowledged.This work has been supported by the research project FIS2011–22566, Ministerio de Ciencia e Innovación, Spain.
NO Ministerio de Ciencia e Innovación (MICINN), España
DS Docta Complutense
RD 8 abr 2025