Logarithmic and power-law entropies from convexity

Kalogeropoulos, Nikolaos

Logarithmic and power-law entropies from convexity

Nikolaos Kalogeropoulos

Jun 25, 2024

12 pages

e-Print:

2406.17411 [cond-mat.stat-mech]

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Abstract: (arXiv)

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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12 pages. No figures. Standard LaTeX2e

References(22)

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