Please use this identifier to cite or link to this item:
http://hdl.handle.net/2381/4266
Title: | Basic Types of Coarse-Graining |
Authors: | Gorban, Alexander N. |
First Published: | 2006 |
Publisher: | Dept. of Mathematics, University of Leicester |
Abstract: | Summary. 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 ε-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 ε-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 semi-groups 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. |
Series/Report no.: | MA 06-007 |
Links: | http://www2.le.ac.uk/departments/mathematics/extranet/research-material/reports/res_rep06 http://hdl.handle.net/2381/4266 |
Type: | Report |
Appears in Collections: | Reports, Dept. of Mathematics |
Files in This Item:
File | Description | Size | Format | |
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MA-06-007.pdf | 657.73 kB | Adobe PDF | View/Open |
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