### Impacto

### Downloads

Downloads per month over past year

Jensen, Henrik Jeldtoft and Tempesta, Piergiulio
(2018)
*Group entropies: from phase space geometry to entropy functionals via Group Theory.*
Entropy, 20
(10).
ISSN 1099-4300

Preview |
PDF
Creative Commons Attribution. 268kB |

Official URL: http://dx.doi.org/10.3390/e20100804

## Abstract

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.

Item Type: | Article |
---|---|

Additional Information: | ©2018 by the authors. |

Uncontrolled Keywords: | Statistical-mechanics; Zeta-functions; Formal group; Generalised entropies; Formal groups; Phase space growth rate |

Subjects: | Sciences > Physics > Physics-Mathematical models Sciences > Physics > Mathematical physics |

ID Code: | 50580 |

Deposited On: | 21 Dec 2018 19:40 |

Last Modified: | 08 Jan 2019 09:34 |

### Origin of downloads

Repository Staff Only: item control page