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.

Department of Mathematics FNSPE Czech Technical University Trojanova 13 12000 Prague Czech Republic

École Polytechnique de Montréal C P 6079 suc Centre ville Montréal QC H3C3A7 Canada

Mathematical Institute Faculty of Mathematics and Physics Charles University Sokolovská 83 18675 Prague Czech Republic

Weierstrass Institute Mohrenstrasse 39 10117 Berlin Germany

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Dynamic and Renormalization-Group Extensions of the Landau Theory of Critical Phenomena

Gradient and GENERIC time evolution towards reduced dynamics