2003/07/31 by Petr Jizba, Toshihico Arimitsu · 3 citations
Economics, Econometrics and Finance · Mathematics · Neuroscience · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Applied mathematics #Artificial intelligence #Bhattacharyya distance #Complex Systems and Time Series Analysis #Computer science #Data mining #Entropy (arrow of time) #Granularity #Mathematics #Measure (data warehouse) #Neural dynamics and brain function #Observability #Observable #Physics #Principle of maximum entropy #Quantum mechanics #Rényi entropy #Statistical physics #Statistics #cond-mat.stat-mech #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1103/physreve.69.026128
published as Phys.Rev. E69 (2004) 026128 · 18 pages, 1 EPS figure, REVTeX, minor changes, accepted to Phys. Rev. E
arxiv created 2003/12/21 · openalex publication_date 2004/02/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Despite recent claims we argue that Rényi's entropy is an observable quantity. It is shown that, contrary to popular belief, the reported domain of instability for Rényi entropies has zero measure (Bhattacharyya measure). In addition, we show that the instabilities can be easily emended by introducing a coarse graining into an actual measurement. We also clear up any doubts regarding the observability of Rényi's entropy in (multi)fractal systems and in systems with absolutely continuous probability density functions.