Logarithmic and power-law entropies from convexity
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916299772264448 |
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| author | Kalogeropoulos, Nikolaos |
| author_facet | Kalogeropoulos, Nikolaos |
| contents | In an attempt to understand the origin and robustness of the Boltzmann/Gibbs/Shannon entropic functional, we adopt a geometric approach and discuss the implications of the Johnson-Lindenstrauss lemma and of Dvoretzky's theorem on convex bodies for the choice of this functional form. We contrast these results with a more recent result on flowers of balls, which may be interpreted as suggesting the use of power-law entropies for some systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17411 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Logarithmic and power-law entropies from convexity Kalogeropoulos, Nikolaos Statistical Mechanics High Energy Physics - Theory Mathematical Physics Probability History and Philosophy of Physics In an attempt to understand the origin and robustness of the Boltzmann/Gibbs/Shannon entropic functional, we adopt a geometric approach and discuss the implications of the Johnson-Lindenstrauss lemma and of Dvoretzky's theorem on convex bodies for the choice of this functional form. We contrast these results with a more recent result on flowers of balls, which may be interpreted as suggesting the use of power-law entropies for some systems. |
| title | Logarithmic and power-law entropies from convexity |
| topic | Statistical Mechanics High Energy Physics - Theory Mathematical Physics Probability History and Philosophy of Physics |
| url | https://arxiv.org/abs/2406.17411 |