RT Journal Article
T1 Group entropies: from phase space geometry to entropy functionals via Group Theory
A1 Jensen, Henrik Jeldtoft
A1 Tempesta, Piergiulio
AB The entropy of Boltzmann-Gibbs, as proved by Shannon and Khinchin, is based on four axioms, where the fourth one concerns additivity. The group theoretic entropies make use of formal group theory to replace this axiom with a more general composability axiom. As has been pointed out before, generalised entropies crucially depend on the number of allowed degrees of freedom N. The functional form of group entropies is restricted (though not uniquely determined) by assuming extensivity on the equal probability ensemble, which leads to classes of functionals corresponding to sub-exponential, exponential or super-exponential dependence of the phase space volume W on N. We review the ensuing entropies, discuss the composability axiom and explain why group entropies may be particularly relevant from an information-theoretical perspective.
PB MDPI
SN 1099-4300
YR 2018
FD 2018-10-19
LK https://hdl.handle.net/20.500.14352/12966
UL https://hdl.handle.net/20.500.14352/12966
LA eng
NO ©2018 by the authors.This research of P.T. has been partly supported by the research project FIS2015-63966, MINECO, Spain, and by the ICMAT Severo Ochoa project SEV-2015-0554 (MINECO).
NO Ministerio de Economía y Competitividad (MINECO)
NO ICMAT
DS Docta Complutense
RD 15 dic 2025