Chaos, Nonlinearity, Complexity: The Dynamical Paradigm of Nature

A. Sengupta (editor)3540317562, 9783540317562, 9783540317579

This carefully edited book presents a focused debate on the mathematics and physics of chaos, nonlinearity and complexity in nature. It explores the role of non-extensive statistical mechanics in non-equilibrium thermodynamics, and presents an overview of the strong nonlinearity of chaos and complexity in natural systems that draws on the relevant mathematics from topology, measure-theory, inverse and ill-posed problems, set-valued analysis, and nonlinear functional analysis. It presents a self-contained scientific theory of complexity and complex systems as the steady state of non-equilibrium systems, denoting a homeostatic dynamic equilibrium between stabilizing order and destabilizing disorder.

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Table of contents :
Chaos, Periodicity and Complexity on Dynamical Systems….Pages 1-52
Foundations of Nonextensive Statistical Mechanics….Pages 53-71
Critical Attractors and the Physical Realm of q -statistics….Pages 72-113
Non-Boltzmannian Entropies for Complex Classical Systems, Quantum Coherent States and Black Holes….Pages 114-161
Power Law and Tsallis Entropy: Network Traffic and Applications….Pages 162-178
The Role of Chaos and Resonances in Brownian Motion….Pages 179-206
Models of Finite Bath and Generalised Thermodynamics….Pages 207-217
Quantum Black Hole Thermodynamics….Pages 218-246
Complexity in Organizations: A Paradigm Shift….Pages 247-269
Chaos, Nonlinearity, Complexity: A Unified Perspective….Pages 270-352