Hyperstatistics
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914512523755520 |
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| author | Squillante, Lucas Soares, Samuel M. Tsallis, Constantino de Souza, Mariano |
| author_facet | Squillante, Lucas Soares, Samuel M. Tsallis, Constantino de Souza, Mariano |
| contents | We propose a general approach, named by us hyperstatistics, to treat complex systems, in which Boltzmann-Gibbs statistics breaks down in domains of the system. Hyperstatistics preserves the concavity of nonadditive $q$-entropy. We obtain analytical closed-form expressions for the here proposed $q$-generalized Boltzmann factor $B_q$ considering uniform, $γ$, Log-normal, F, and the $q$-$γ$ probability distribution functions. Remarkably, for all investigated distribution functions, $B_q$ reduces to a $q$-exponential-type function. To demonstrate the applicability of hyperstatistics, we use a table top experiment of the discharge of a capacitor considering $γ$-distributed relaxation times, the pressure decay over time associated with the pumping of $^4$He lines of a closed cycle cryostat, midrapidity data for $p$-Pb collisions at the LHC, as well as data set for acceleration distribution in turbulent systems. Furthermore, we deduce the power-law-like dielectric response using the $q$-$γ$-distribution function. Our proposal is applicable to systems with inherent non-Boltzmann-Gibbsian statistics in domains of the system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24783 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hyperstatistics Squillante, Lucas Soares, Samuel M. Tsallis, Constantino de Souza, Mariano Statistical Mechanics High Energy Physics - Experiment High Energy Physics - Theory Nuclear Theory Accelerator Physics Data Analysis, Statistics and Probability Instrumentation and Detectors We propose a general approach, named by us hyperstatistics, to treat complex systems, in which Boltzmann-Gibbs statistics breaks down in domains of the system. Hyperstatistics preserves the concavity of nonadditive $q$-entropy. We obtain analytical closed-form expressions for the here proposed $q$-generalized Boltzmann factor $B_q$ considering uniform, $γ$, Log-normal, F, and the $q$-$γ$ probability distribution functions. Remarkably, for all investigated distribution functions, $B_q$ reduces to a $q$-exponential-type function. To demonstrate the applicability of hyperstatistics, we use a table top experiment of the discharge of a capacitor considering $γ$-distributed relaxation times, the pressure decay over time associated with the pumping of $^4$He lines of a closed cycle cryostat, midrapidity data for $p$-Pb collisions at the LHC, as well as data set for acceleration distribution in turbulent systems. Furthermore, we deduce the power-law-like dielectric response using the $q$-$γ$-distribution function. Our proposal is applicable to systems with inherent non-Boltzmann-Gibbsian statistics in domains of the system. |
| title | Hyperstatistics |
| topic | Statistical Mechanics High Energy Physics - Experiment High Energy Physics - Theory Nuclear Theory Accelerator Physics Data Analysis, Statistics and Probability Instrumentation and Detectors |
| url | https://arxiv.org/abs/2604.24783 |