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Updated: Apr 27, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
7.6K
Generalized extensive entropies for studying dynamical systems in highly anisotropic phase spaces
Giorgio Sonnino1, György Steinbrecher2
1Université Libre de Bruxelles (ULB), Department of Physics, Bvd du Triomphe, Campus de la Plaine CP 231, 1050 Brussels, Belgium and Royal Military School (RMS), Av. de la Renaissance 30, 1000 Brussels, Belgium.
Summary
Generalized Rényi entropies offer new insights into dynamical systems. These advanced entropy measures act as Liapunov functionals, crucial for understanding systems with random perturbations.
Area of Science:
- Statistical mechanics
- Dynamical systems theory
- Information theory
Background:
- Rényi entropy provides a framework for quantifying uncertainty and information.
- Understanding the behavior of complex systems, especially those with random elements, is a significant challenge.
Purpose of the Study:
- To introduce and explore generalized Rényi entropies.
- To determine the probability distribution function derived from these generalized entropies using the Maximum Entropy (MaxEnt) principle.
- To establish the role of these generalized entropies as Liapunov functionals in dynamical systems.
Main Methods:
- Geometrical interpretation of Rényi entropy.
- Application of the Maximum Entropy (MaxEnt) principle with generalized entropies.
- Analysis of dynamical systems subjected to random perturbations.
Main Results:
- Derived the probability distribution function using generalized entropies and the MaxEnt principle.
- Proved that generalized Rényi entropies function as Liapunov functionals for a broad range of dynamical systems with random perturbations.
- Illustrated the applicability of generalized Rényi entropies with physical examples, such as particle transport in random media.
Conclusions:
- Generalized Rényi entropies offer a powerful tool for analyzing complex systems.
- The connection to Liapunov functionals highlights their utility in stability analysis of perturbed dynamical systems.
- These entropies have broad applications in physics and related fields.
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