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Open AccessArticle

Dynamic Maximum Entropy Reduction

1
Department of Mathematics—FNSPE, Czech Technical University, Trojanova 13, 12000 Prague, Czech Republic
2
Mathematical Institute, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 18675 Prague, Czech Republic
3
Weierstrass Institute, Mohrenstrasse 39, 10117 Berlin, Germany
4
École Polytechnique de Montréal, C.P.6079 suc. Centre-ville, Montréal, QC H3C3A7, Canada
*
Author to whom correspondence should be addressed.
Entropy 2019, 21(7), 715; https://doi.org/10.3390/e21070715
Received: 28 June 2019 / Revised: 18 July 2019 / Accepted: 19 July 2019 / Published: 22 July 2019
(This article belongs to the Special Issue Entropy and Non-Equilibrium Statistical Mechanics)
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Abstract

Any physical system can be regarded on different levels of description varying by how detailed the description is. We propose a method called Dynamic MaxEnt (DynMaxEnt) that provides a passage from the more detailed evolution equations to equations for the less detailed state variables. The method is based on explicit recognition of the state and conjugate variables, which can relax towards the respective quasi-equilibria in different ways. Detailed state variables are reduced using the usual principle of maximum entropy (MaxEnt), whereas relaxation of conjugate variables guarantees that the reduced equations are closed. Moreover, an infinite chain of consecutive DynMaxEnt approximations can be constructed. The method is demonstrated on a particle with friction, complex fluids (equipped with conformation and Reynolds stress tensors), hyperbolic heat conduction and magnetohydrodynamics. View Full-Text
Keywords: model reduction; non-equilibrium thermodynamics; MaxEnt; dynamic MaxEnt; complex fluids; heat conduction; Ohm’s law model reduction; non-equilibrium thermodynamics; MaxEnt; dynamic MaxEnt; complex fluids; heat conduction; Ohm’s law
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Klika, V.; Pavelka, M.; Vágner, P.; Grmela, M. Dynamic Maximum Entropy Reduction. Entropy 2019, 21, 715.

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