Basic Types of Coarse-Graining

A. N. Gorban

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arXiv · cond-mat/0602024

Basic Types of Coarse-Graining

A. N. Gorban

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Abstract

We consider two basic types of coarse-graining: the Ehrenfests' coarse-graining and its extension to a general principle of non-equilibrium thermodynamics, and the coarse-graining based on uncertainty of dynamical models and Epsilon-motions (orbits). Non-technical discussion of basic notions and main coarse-graining theorems are presented: the theorem about entropy overproduction for the Ehrenfests' coarse-graining and its generalizations, both for conservative and for dissipative systems, and the theorems about stable properties and the Smale order for Epsilon-motions of general dynamical systems including structurally unstable systems. Computational kinetic models of macroscopic dynamics are considered. We construct a theoretical basis for these kinetic models using generalizations of the Ehrenfests' coarse-graining. General theory of reversible regularization and filtering semigroups in kinetics is presented, both for linear and non-linear filters. We obtain explicit expressions and entropic stability conditions for filtered equations. A brief discussion of coarse-graining by rounding and by small noise is also presented.

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A. N. Gorban. 2006-03-09. Basic Types of Coarse-Graining. https://arxiv.org/abs/cond-mat/0602024

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