Thermodynamic Explanation of Landau Damping by Reduction to Hydrodynamics

Pavelka, Michal; Klika, Václav; Grmela, Miroslav

doi:10.3390/e20060457

Cited by 8 publications

(10 citation statements)

References 33 publications

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“…There is no general model reduction technique applicable to all systems. However, many physically based (we do not focus on formal mathematical expansion methods although we make a certain comparison below) methods have been developed, such as the Chapman-Enskog expansion [1] or other series expansions [2], projector operator techniques [3,4], or the method of natural projector, invariant slow manifolds, entropic scalar product and Ehrenfest reduction [5][6][7][8]. A common feature of the reduction techniques is the recognition of entropy, since entropy (measuring unavailable information) grows during the passage from the more detailed level to the less detailed.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Maximum Entropy Reduction

Klika

Pavelka

Vágner

et al. 2019

Entropy

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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.

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Section: Introductionmentioning

confidence: 99%

Dynamic Maximum Entropy Reduction

Klika

Pavelka

Vágner

et al. 2019

Entropy

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“…The hydrodynamic fields are unaffected explicitly by the scaling yielding the governing equations of the modified Poisson-Grad hierarchy Note that no dissipative evolution appears in the equation for the total spatial energy density due to the entropy production term as discussed above. The Fokker-Planck-like dissipation can be seen as derivative of dissipation potential [37]; and (ii) it is anticipated that fast oscillations in the v−space develop due to phenomena related to the Landau damping [34,[40][41][42].…”

Section: (F) Reduction To Hydrodynamic Fieldsmentioning

confidence: 99%

Gradient and GENERIC time evolution towards reduced dynamics

Grmela

Klika

Pavelka

2020

Phil. Trans. R. Soc. A.

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Reduction of a mesoscopic dynamical theory to equilibrium thermodynamics brings to the latter theory the fundamental thermodynamic relation (i.e. entropy as a function of the thermodynamic state variables). The reduction is made by following the mesoscopic time evolution to its conclusion, i.e. to fixed points at which the time evolution ceases to continue. The approach to fixed points is driven by entropy, that, if evaluated at the fixed points, becomes the thermodynamic entropy. Since the fixed points are parametrized by the thermodynamic state variables (by constants of motion), the thermodynamic entropy arises as a function of the thermodynamic state variables and thus the final outcome of the reduction is the fundamental thermodynamic relation. This reduction process extends also to reductions in which the reduced theory still involves the time evolution (e.g. reduction of kinetic theory to hydrodynamics). The essence of the extension is the replacement of the mesoscopic time evolution of the state variables with the corresponding mesoscopic time evolution of the vector field (i.e. of the fluxes). The fixed point in this flux time evolution is the vector field generating the reduced mesoscopic time evolution. The flux-entropy driving the flux time evolution becomes, if evaluated at the fixed point, the flux fundamental thermodynamic relation in the reduced dynamical theory. We show that the flux-entropy is a potential related to the entropy production. This article is part of the theme issue ‘Fundamental aspects of nonequilibrium thermodynamics’.

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“…MaxEnt then provides the embedding of N into M as usually. The vector field on M does not need to have the GENERIC structure, but it is advantageous as shown in [36].…”

Section: Reduced Dynamicsmentioning

confidence: 99%

Learning Physics from Data: a Thermodynamic Interpretation

Chinesta¹,

Grmela²,

Moya³

et al. 2019

Preprint

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Experimental data bases are typically very large and high dimensional. To learn from them requires to recognize important features (a pattern), often present at scales different to that of the recorded data. Following the experience collected in statistical mechanics and thermodynamics, the process of recognizing the pattern (the learning process) can be seen as a dissipative time evolution driven by entropy. This is the way thermodynamics enters machine learning. Learning to handle free surface liquids serves as an illustration.

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Thermodynamic Explanation of Landau Damping by Reduction to Hydrodynamics

Cited by 8 publications

References 33 publications

Dynamic Maximum Entropy Reduction

Dynamic Maximum Entropy Reduction

Gradient and GENERIC time evolution towards reduced dynamics

Learning Physics from Data: a Thermodynamic Interpretation

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