The entropy functional, the information path functional's essentials and\n their connections to Kolmogorov's entropy, complexity and physics

2011/07/08 by Vladimir S. Lerner, Lerner, Vladimir S.
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Information Theory (cs.IT) #Optimization and Control (math.OC) #Quantum chaos and dynamical systems #Statistical Mechanics and Entropy #Statistics Theory (math.ST) #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.1107.1739

openalex publication_date 2011/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paper introduces the recent results related to an entropy functional on\ntrajectories of a controlled diffusion process, and the information path\nfunctional (IPF), analyzing their connections to the Kolmogorov's entropy,\ncomplexity and the Lyapunov's characteristics. Considering the IPF's essentials\nand specifics, the paper studies the singularities of the IPF extremal\nequations and the created invariant relations, which both are useful for the\nsolution of important mathematical and applied problems.\n Keywords: Additive functional; Entropy; Singularities, Natural Border\nProblem; Invariant\n

Citations

• Information heat engine: converting information to energy by feedback control
• A universal instability of many-dimensional oscillator systems

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