Extensive composable entropy for the analysis of cosmological data
In recent decades, an intensive worldwide research activity is focusing both black holes and cosmos (e.g. the dark-energy phenomenon) on the basis of entropic approaches. The Boltzmann-Gibbs-based Bekenstein-Hawking entropy SBH∝A/lP2 (A≡ area; lP≡ Planck length) systematically plays a crucial theore...
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Elsevier
2025-02-01
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| Series: | Physics Letters B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0370269324007962 |
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| author | Constantino Tsallis Henrik Jeldtoft Jensen |
| author_facet | Constantino Tsallis Henrik Jeldtoft Jensen |
| author_sort | Constantino Tsallis |
| collection | DOAJ |
| description | In recent decades, an intensive worldwide research activity is focusing both black holes and cosmos (e.g. the dark-energy phenomenon) on the basis of entropic approaches. The Boltzmann-Gibbs-based Bekenstein-Hawking entropy SBH∝A/lP2 (A≡ area; lP≡ Planck length) systematically plays a crucial theoretical role although it has a serious drawback, namely that it violates the thermodynamic extensivity of spatially-three-dimensional systems. Still, its intriguing area dependence points out the relevance of considering the form W(N)∼μNγ(μ>1;γ>0), W and N respectively being the total number of microscopic possibilities and the number of components; γ=1 corresponds to standard Boltzmann-Gibbs (BG) statistical mechanics. For this W(N) asymptotic behavior, we make use of the group-theoretic entropic functional Sα,γ=k[lnΣi=1Wpiα1−α]1γ(α∈R;S1,1=SBG≡−k∑i=1Wpilnpi), first derived by P. Tempesta in Chaos 30,123119, (2020). This functional is extensive (as required by thermodynamics) and composable, ∀(α,γ). Being extensive means that in the micro-canonical, or uniform, ensemble where all micro-state occur with the same probability, the entropy becomes proportional to N asymptotically: S(N)∝N for N→∞. An entropy is composable if it satisfies that the entropy SA of a system A=B×C consisting of two statistically independent parts B and C is given in a consistent way as SA=Φ(SB,SC) where the composition function Φ(x,y) is obtained from group-theory.We further show that (α,γ)=(1,2/3) satisfactorily agrees with cosmological data measuring neutrinos, Big Bang nucleosynthesis and the relic abundance of cold dark matter particles, as well as dynamical and geometrical cosmological data sets. |
| format | Article |
| id | doaj-art-66ffa9ef4c154a50a5c6f3f25efe6bd9 |
| institution | Kabale University |
| issn | 0370-2693 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Elsevier |
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| series | Physics Letters B |
| spelling | doaj-art-66ffa9ef4c154a50a5c6f3f25efe6bd92025-02-10T04:33:50ZengElsevierPhysics Letters B0370-26932025-02-01861139238Extensive composable entropy for the analysis of cosmological dataConstantino Tsallis0Henrik Jeldtoft Jensen1Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology of Complex Systems, Rua Xavier Sigaud 150, 22290-180, Rio de Janeiro RJ, Brazil; Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, 87501 NM, USA; Complexity Science Hub Vienna, Metternichgasse 8, 1030 Vienna, Austria; Corresponding author.Centre for Complexity Science and Department of Mathematics, Imperial College London, South Kensington Campus, London, SW7 2AZ, United Kingdom; School of Computer Science, Tokyo Institute of Technology, 4259, Nagatsuta-cho, Yokohama 226-8502, Japan; Complexity Science Hub Vienna, Metternichgasse 8, 1030 Vienna, AustriaIn recent decades, an intensive worldwide research activity is focusing both black holes and cosmos (e.g. the dark-energy phenomenon) on the basis of entropic approaches. The Boltzmann-Gibbs-based Bekenstein-Hawking entropy SBH∝A/lP2 (A≡ area; lP≡ Planck length) systematically plays a crucial theoretical role although it has a serious drawback, namely that it violates the thermodynamic extensivity of spatially-three-dimensional systems. Still, its intriguing area dependence points out the relevance of considering the form W(N)∼μNγ(μ>1;γ>0), W and N respectively being the total number of microscopic possibilities and the number of components; γ=1 corresponds to standard Boltzmann-Gibbs (BG) statistical mechanics. For this W(N) asymptotic behavior, we make use of the group-theoretic entropic functional Sα,γ=k[lnΣi=1Wpiα1−α]1γ(α∈R;S1,1=SBG≡−k∑i=1Wpilnpi), first derived by P. Tempesta in Chaos 30,123119, (2020). This functional is extensive (as required by thermodynamics) and composable, ∀(α,γ). Being extensive means that in the micro-canonical, or uniform, ensemble where all micro-state occur with the same probability, the entropy becomes proportional to N asymptotically: S(N)∝N for N→∞. An entropy is composable if it satisfies that the entropy SA of a system A=B×C consisting of two statistically independent parts B and C is given in a consistent way as SA=Φ(SB,SC) where the composition function Φ(x,y) is obtained from group-theory.We further show that (α,γ)=(1,2/3) satisfactorily agrees with cosmological data measuring neutrinos, Big Bang nucleosynthesis and the relic abundance of cold dark matter particles, as well as dynamical and geometrical cosmological data sets.http://www.sciencedirect.com/science/article/pii/S0370269324007962 |
| spellingShingle | Constantino Tsallis Henrik Jeldtoft Jensen Extensive composable entropy for the analysis of cosmological data Physics Letters B |
| title | Extensive composable entropy for the analysis of cosmological data |
| title_full | Extensive composable entropy for the analysis of cosmological data |
| title_fullStr | Extensive composable entropy for the analysis of cosmological data |
| title_full_unstemmed | Extensive composable entropy for the analysis of cosmological data |
| title_short | Extensive composable entropy for the analysis of cosmological data |
| title_sort | extensive composable entropy for the analysis of cosmological data |
| url | http://www.sciencedirect.com/science/article/pii/S0370269324007962 |
| work_keys_str_mv | AT constantinotsallis extensivecomposableentropyfortheanalysisofcosmologicaldata AT henrikjeldtoftjensen extensivecomposableentropyfortheanalysisofcosmologicaldata |