Logarithmic and power-law entropies from convexity

Nikolaos Kalogeropoulos

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arXiv · 2406.17411

Logarithmic and power-law entropies from convexity

Nikolaos Kalogeropoulos

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Abstract

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.

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Nikolaos Kalogeropoulos. 2024-06-25. Logarithmic and power-law entropies from convexity. https://arxiv.org/abs/2406.17411

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