**Václav Klika 1,\*, Michal Pavelka <sup>2</sup> , Petr Vágner 2,3 and Miroslav Grmela <sup>4</sup>**


Received: 28 June 2019; Accepted: 19 July 2019; Published: 22 July 2019

**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.

**Keywords:** model reduction; non-equilibrium thermodynamics; MaxEnt; dynamic MaxEnt; complex fluids; heat conduction; Ohm's law
