@article{Jensen:2018:10.3390/e20100804,
author = {Jensen, H and Tempesta, P},
doi = {10.3390/e20100804},
journal = {Entropy},
title = {Group entropies: from phase space geometry to entropy functionals via group theory},
url = {http://dx.doi.org/10.3390/e20100804},
volume = {20},
year = {2018}
}

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TY  - JOUR
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.
AU  - Jensen,H
AU  - Tempesta,P
DO  - 10.3390/e20100804
PY  - 2018///
SN  - 1099-4300
TI  - Group entropies: from phase space geometry to entropy functionals via group theory
T2  - Entropy
UR  - http://dx.doi.org/10.3390/e20100804
UR  - http://hdl.handle.net/10044/1/65475
VL  - 20
ER  - 

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