This book explores non-extensive statistical mechanics in
non-equilibrium thermodynamics, and presents an overview of the
strong nonlinearity of chaos and complexity in natural systems,
drawing on relevant mathematics from topology, measure-theory,
inverse and ill-posed problems, set-valued analysis, and nonlinear
functional analysis. It offers a self-contained 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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