New approach to Epsilon-entropy and Its comparison with Kolmogorov's Epsilon-entropy

1998/06/08 by Kei Inoue, Inoue, Kei, Takashi Matsuoka +3
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.quant-ph/9806027

openalex publication_date 1998/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Kolmogorov introduced a concept of Epsilon-entropy to analyze information in classical continuous system. The fractal dimension of geometrical sets was introduced by Mandelbrot as a new criterion to analyze the complexity of these sets. The Epsilon-entropy and the fractal dimension of a state in general quantum system were introduced by one of the present authors in order to characterize chaotic properties of general states. In this paper, we show that Epsilon-entropy of a state includes Kolmogorov Epsilon-entropy, and the fractal dimension of a state describe fractal structure of Gaussian measures.

Citations

• The Fractal Geometry of Nature

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