2024/06/25 by Nikolaos Kalogeropoulos, Kalogeropoulos, Nikolaos
Engineering · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #FOS: Physical sciences #Graph theory and applications #High Energy Physics - Theory (hep-th) #History and Philosophy of Physics (physics.hist-ph) #Mathematical Physics (math-ph) #Probability (math.PR) #Process Optimization and Integration #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2406.17411
openalex publication_date 2024/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.