Most assertions involving Shannon entropy have their Kolmogorov complexity counterparts. A general theorem of Romashchenko [4] states that every information inequality that is valid in Shannon’s theory is also valid in Kolmogorov’s theory, and vice verse. In this paper we prove that this is no longer true for ∀∃-assertions, exhibiting the first example where the formal analogy between Shannon e...

Physical and chemical stochastic processes described by the master equation are investigated. The system-size expansion, called the Ω-expansion, transforms the master equation to the corresponding Fokker-Planck equation. In this paper, we examine the entropy production for both the master equation and the corresponding Fokker-Planck equation. For the master equation, the exact expression of the...

Hierarchy of one and many-parameter families of random trigonometric chaotic maps and one-parameter random elliptic chaotic maps of cn type with an invariant measure have been introduced. Using the invariant measure (Sinai-Ruelle-Bowen measure), the Kolmogrov-Sinai entropy of the random chaotic maps have been calculated analytically, where the numerical simulations support the results .

Physical and chemical stochastic processes described by the master equation are investigated. The system-size expansion, called the Ω-expansion, trasnforms the master equation to the corresponding Fokker-Planck equation. In this paper, we examine the entropy production both for the master equation and for the corresponding Fokker-Planck equation. For the master equation, the exact expression of...

This paper presents a taxonomy and overview of approaches to the measurement of graph and network complexity. The taxonomy distinguishes between deterministic (e.g., Kolmogorov complexity) and probabilistic approaches with a view to placing entropy-based probabilistic measurement in context. Entropy-based measurement is the main focus of the paper. Relationships between the different entropy fu...

Precisely describing the formation and evolution rules of coal-rock fracturing crack have great value on reservoir fracturing improvement and highly efficient mining of coal bed methane well. In this paper, a non-linear dynamic method is used to study crack damage evolution behavior of coal-rock fracturing. Considering distribution characteristics of natural cracks in coal-rock, and based on da...

Kolmogorov introduced a concept of ε-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 ε-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...

We study the quantum-classical correspondence for systems with interacting spin-particles that are strongly chaotic in classical limit. This is done presence of constants motion associated fixed angular momenta individual spins. Our analysis Lyapunov spectra reveals largest exponent agrees determines local instability each spin moving under influence all other Within this picture, we introduce ...

Kolmogorov introduced a concept of ε-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 ε-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...