A new entropy based on a group-theoretical structure

Simple item page
dc.contributor.authorCurado, Evaldo M. F.
dc.contributor.authorTempesta, Piergiulio
dc.contributor.authorTsallis, Constantino
dc.date.accessioned2023-06-18T06:51:30Z
dc.date.available2023-06-18T06:51:30Z
dc.date.issued2016-03
dc.description© 2016 Elsevier Inc. The research of P. T. has been partly supported by the research project FIS2011–22566, Ministerio de Ciencia e Innovación, Spain. Partial financial support by CNPq and Faperj (Brazilian agencies), and by the John Templeton Foundation is acknowledged as well.
dc.description.abstractA multi-parametric version of the nonadditive entropy S_q is introduced. This new entropic form, denoted by S_a,b,r, possesses many interesting statistical properties, and it reduces to the entropy S_q for b=0, a=r:=1−q (hence Boltzmann–Gibbs entropy S_BG for b=0, a=r→0). The construction of the entropy S_a,b,r is based on a general group-theoretical approach recently proposed by one of us, Tempesta (2016). Indeed, essentially all the properties of this new entropy are obtained as a consequence of the existence of a rational group law, which expresses the structure of S_a,b,r with respect to the composition of statistically independent subsystems. Depending on the choice of the parameters, the entropy S_a,b,r can be used to cover a wide range of physical situations, in which the measure of the accessible phase space increases say exponentially with the number of particles NN of the system, or even stabilizes, by increasing NN, to a limiting value. This paves the way to the use of this entropy in contexts where the size of the phase space does not increase as fast as the number of its constituting particles (or subsystems) increases.
dc.description.departmentDepto. de Física Teórica
dc.description.facultyFac. de Ciencias Físicas
dc.description.refereedTRUE
dc.description.sponsorshipMinisterio de Ciencia e Innovación (MICINN), España
dc.description.sponsorshipConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Brasil
dc.description.sponsorshipFundação de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ), Brasil
dc.description.sponsorshipJohn Templeton Foundation
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/37113
dc.identifier.citation[1] S. Abe, Generalized entropy optimized by a given arbitrary distribution, J. Phys. A: Math. Gen. 36 8733{8738 (2003). [2] C. Beck and E. D. G. Cohen, Superstatistics, Physica A 322 267{275 (2003). [3] S. Bochner, Formal Lie groups, Ann. Math. 47, 192{201 (1946). [4] E. P. Borges and I. Roditi, A family of nonextensive entropies, Phys. Lett. A 246 399{402 (1998). [5] V. M. Bukhshtaber, A. S. Mishchenko and S. P. Novikov, Formal groups and their role in the apparatus of algebraic topology, Uspehi Mat. Nauk 26, 2, 161{154 (1971), transl. Russ. Math. Surv. 26, 63{90 (1971). [6] H. B. Callen, Thermodynamics and an Introduction to Thermostatistics, II edition, John Wiley and Sons (1985). [7] R. Hanel and S. Thurner, A comprehensive classification of complex statistical systems and an axiomatic derivation of their entropy and distribution functions, Europhys. Lett. 93 20006 (2011). [8] R. Hanel, S. Thurner and M. Gell-Mann, How multiplicity determines en- tropy: derivation of the maximum entropy principle for complex systems, PNAS 111 (19), 6905{6910 (2014). [9] M. Hazewinkel, Formal Groups and Applications, Academic Press, New York (1978). [10] G. Kaniadakis, Statistical mechanics in the context of special relativity, Phys. Rev. E 66 056125 (2002). [11] A. I. Khinchin, Mathematical Foundations of Information Theory, Dover, New York, 1957. [12] J. Naudts, Generalised exponential families and associated entropy func- tions, Entropy, 10, 131{149 (2008). [13] C. E. Shannon, A mathematical theory of communication, Bell Syst. Tech. J. 27 (1948) 379{423, 27 623{653 (1948). [14] C. Shannon, W. Weaver, The mathematical Theory of Communication, University of Illinois Press, Urbana, IL, 1949. [15] P. Tempesta, Group entropies, correlation laws and zeta functions, Phys. Rev. E 84, 021121 (2011). [16] P. Tempesta, Beyond the Shannon-Khinchin Formulation: The Compos- ability Axiom and the Universal Group Entropy, arXiv: 1407.3807 (2014). [17] P. Tempesta, A theorem on the existence of generalized trace-form entropies (unpublished work), (2015). [18] C. Tsallis, Possible generalization of the Boltzmann{Gibbs statistics, J. Stat. Phys. 52, Nos. 1/2, 479{487 (1988). [19] C. Tsallis, Introduction to Nonextensive Statistical Mechanics{Approaching a Complex World, Springer, Berlin (2009). [20] C. Tsallis, L. Cirto, Black hole thermodynamical entropy, Eur. Phys. J. C 73, 2487 (2013).
dc.identifier.doi10.1016/j.aop.2015.12.008
dc.identifier.issn0003-4916
dc.identifier.officialurlhttp://dx.doi.org/10.1016/j.aop.2015.12.008
dc.identifier.relatedurlhttp://www.sciencedirect.com
dc.identifier.relatedurlhttp://arxiv.org/abs/1507.05058
dc.identifier.urihttps://hdl.handle.net/20.500.14352/24419
dc.journal.titleAnnals of physics
dc.language.isoeng
dc.page.final31
dc.page.initial22
dc.publisherElsevier Masson
dc.relation.projectIDFIS2011-22566
dc.rights.accessRightsopen access
dc.subject.cdu51-73
dc.subject.keywordGeneralized entropies
dc.subject.keywordGroup theory
dc.subject.keywordStatistical mechanics.
dc.subject.ucmFísica-Modelos matemáticos
dc.subject.ucmFísica matemática
dc.titleA new entropy based on a group-theoretical structure
dc.typejournal article
dc.volume.number366
dspace.entity.typePublication
relation.isAuthorOfPublication46e9a666-a5cf-44c3-8726-7cbe2c61bd1a
relation.isAuthorOfPublication.latestForDiscovery46e9a666-a5cf-44c3-8726-7cbe2c61bd1a
Download
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
tempesta22preprint.pdf
Size:
3.41 MB
Format:
Adobe Portable Document Format
downoload Download
Collections
Artículos