Basic Types of Coarse-Graining
| dc.creator | Gorban, A. N. | |
| dc.date | 2006-02-01 | |
| dc.date | 2006-03-09 | |
| dc.date.accessioned | 2026-07-07T07:01:25Z | |
| dc.date.available | 2026-07-07T07:01:25Z | |
| dc.description | 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. | |
| dc.description | 60 pgs, 11 figs., includes new analysis of coarse-graining by filtering. A talk given at the research workshop: "Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena," University of Leicester, UK, August 24-26, 2005 | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0602024 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0602024 | |
| dc.identifier | In: Model Reduction and Coarse--Graining Approaches for Multiscale Phenomena, Ed. by A.N. Gorban, N. Kazantzis, I.G. Kevrekidis, H.C. Öttinger, C. Theodoropoulos, Springer, Berlin-Heidelberg-New York, 2006, 117-176. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/108266 | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Materials Science | |
| dc.title | Basic Types of Coarse-Graining | |
| dc.type | text |