Extensive Composable Entropy for the Analysis of Cosmological Data
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917751459676160 |
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| author | Tsallis, Constantino Jensen, Henrik Jeldtoft |
| author_facet | Tsallis, Constantino Jensen, Henrik Jeldtoft |
| contents | Along 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 $S_{BH}\propto A/l_P^2$ ($A \equiv$ area; $l_P \equiv$ 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 $W(N)\sim μ^{N^γ}\;\;(μ>1;γ>0)$, $W$ 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 introduce here, on a group-theory basis, the entropic functional $S_{α,γ}=k \Bigl[ \frac{\ln Σ_{i=1}^W p_i^α}{1-α} \Bigr]^{\frac{1}γ} \;(α\in \mathbb{R};\,S_{1,1}=S_{BG}\equiv-k\sum_{i=1}^W p_i \ln p_i)$. This functional simultaneously is {\it extensive} (as required by thermodynamics) and {\it composable} (as required for logic consistency), $\forall (α,γ)$. 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 | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_08820 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Extensive Composable Entropy for the Analysis of Cosmological Data Tsallis, Constantino Jensen, Henrik Jeldtoft Statistical Mechanics Along 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 $S_{BH}\propto A/l_P^2$ ($A \equiv$ area; $l_P \equiv$ 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 $W(N)\sim μ^{N^γ}\;\;(μ>1;γ>0)$, $W$ 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 introduce here, on a group-theory basis, the entropic functional $S_{α,γ}=k \Bigl[ \frac{\ln Σ_{i=1}^W p_i^α}{1-α} \Bigr]^{\frac{1}γ} \;(α\in \mathbb{R};\,S_{1,1}=S_{BG}\equiv-k\sum_{i=1}^W p_i \ln p_i)$. This functional simultaneously is {\it extensive} (as required by thermodynamics) and {\it composable} (as required for logic consistency), $\forall (α,γ)$. 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. |
| title | Extensive Composable Entropy for the Analysis of Cosmological Data |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2408.08820 |