1998/04/09 by Italo Guarneri, Guarneri, Italo
Computer Science · Mathematics · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #Dimension (graph theory) #Dimension function #Entropy (arrow of time) #FOS: Physical sciences #Fractal #Fractal dimension #Geometry #Hausdorff dimension #Hausdorff measure #Mathematical Physics (math-ph) #Mathematical analysis #Mathematics #Minkowski–Bouligand dimension #Neural Networks and Applications #Packing dimension #Physics #Pure mathematics #Quantum #Quantum entanglement #Quantum mechanics #Scaling #Spectral density #Statistical physics #Statistics #Von Neumann entropy #chao-dyn #math-ph #math.MP #nlin.CD
paper · pdf · doi:10.48550/arxiv.math-ph/9804009
19 pages, LaTex, to appear in Ann. Inst. H. Poincare'
arxiv created 1998/04/09 · openalex publication_date 1998/04/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Time averaging over the trajectory of a wavepacket up to time T defines a statistical operator (density matrix). The corresponding (Von Neumann) entropy is proven to asymptotically increase with time like D.log T, with D the Hausdorff dimension of the Local Density of States, at least if the latter measure has good scaling properties. In more general cases, spectral upper and lower bounds for the increase of entropy are given, in terms of the Hausdorff and of the Fractal Dimension of the Local Density of States.