RT Journal Article
T1 Formal groups and Z-entropies
A1 Tempesta, Piergiulio
AB We shall prove that the celebrated Renyi entropy is the first example of a new family of infinitely many multi-parametric entropies. We shall call them the Z-entropies. Each of them, under suitable hypotheses, generalizes the celebrated entropies of Boltzmann and Renyi. A  rucial aspect is that every Z-entropy is composable (Tempesta 2016 Ann. Phys. 365, 180-197. (doi: 10.1016/j.aop.2015.08.013)). This property means that the entropy of a system which is composed of two or more independent systems depends, in all the associated probability space, on the choice of the two systems only. Further properties are also required to describe the composition process in terms of a group law. The composability axiom, introduced as a generalization of the fourth Shannon-Khinchin axiom (postulating additivity), is a highly non- trivial requirement. Indeed, in the trace-form class, the Boltzmann entropy and Tsallis entropy are the only known composable cases. However, in the non-trace form class, the Z-entropies arise as new entropic functions possessing the mathematical properties necessary for information-theoretical applications, in both classical and quantum contexts. From a mathematical point of view, composability is intimately related to formal group theory of algebraic topology. The underlying group-theoretical structure determines crucially the statistical properties of the corresponding entropies.
PB Royal Society of London
SN 1364-5021
YR 2016
FD 2016-11-01
LK https://hdl.handle.net/20.500.14352/17652
UL https://hdl.handle.net/20.500.14352/17652
LA eng
NO This work has been partly supported by the research project FIS2015-63966, MINECO, Spain, and by the ICMAT Severo Ochoa project SEV-2015-0554 (MINECO).I wish to thank J. A. Carrasco, A. González López, M. A. Rodríguez and G. Sicuro for useful discussions.
NO Ministerio de EConomía y Competitividad (MINECO)
NO ICMAT Severo Ochoa project (MINECO)
DS Docta Complutense
RD 15 ago 2024