Gradient Dynamics and Entropy Production Maximization

Janečka, Adam; Pavelka, Michal

doi:10.1515/jnet-2017-0005

Cited by 13 publications

(9 citation statements)

References 37 publications

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“…This is guaranteed for instance for convex dissipation potentials, but also non-convexity far from the origin (equilibrium) be taken into account [57]. Moreover, it is in close relation to the method of entropy production maximization [58]. Gradient dynamics plays a key role when formulating dissipation in the GENERIC framework.…”

Section: Dissipation Potentialmentioning

confidence: 90%

Multiscale thermodynamics of charged mixtures

Vágner

Pavelka

Esen

2020

Continuum Mech. Thermodyn.

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A multiscale theory of interacting continuum mechanics and thermodynamics of mixtures of fluids, electrodynamics, polarization, and magnetization is proposed. The mechanical (reversible) part of the theory is constructed in a purely geometric way by means of semidirect products. This leads to a complex Hamiltonian system with a new Poisson bracket, which can be used in principle with any energy functional. The thermodynamic (irreversible) part is added as gradient dynamics, generated by derivatives of a dissipation potential, which makes the theory part of the GENERIC framework. Subsequently, Dynamic MaxEnt reductions are carried out, which lead to reduced GENERIC models for smaller sets of state variables. Eventually, standard engineering models are recovered as the low-level limits of the detailed theory. The theory is then compared to recent literature.

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Section: Dissipation Potentialmentioning

confidence: 90%

Multiscale thermodynamics of charged mixtures

Vágner

Pavelka

Esen

2020

Continuum Mech. Thermodyn.

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“…Appendix B, but it can also be non-convex without violating the second law [32]. Gradient dynamics is in close relation with entropy production maximization [33,34,35] and the steepest entropy ascent (SEA) [36].…”

Section: Generic On the Upper Levelmentioning

confidence: 95%

Generalization of the dynamical lack-of-fit reduction

Pavelka,

Klika,

Grmela

2019

Preprint

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The lack-of-fit statistical reduction, developed and formulated first by Bruce Turkington, is a general method for taking Liouville equation for probability density (detailed level) and transforming it to reduced dynamics of projected quantities. In this paper the method is generalized. The Hamiltonian Liouville equation is replaced by an arbitrary Hamiltonian evolution combined with gradient dynamics (GENERIC), the Boltzmann entropy is replaced by an arbitrary entropy, and the kinetic energy by an arbitrary energy. The gradient part is a generalized gradient dynamics generated by a dissipation potential. The reduced evolution of the projected state variables is shown to preserve the GENERIC structure of the original (detailed level) evolution.

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“…In this picture, reversible part of the dynamics is governed by a Hamiltonian system, [29] whereas irreversible part is governed by a gradient system. We cite a recent study on the gradient systems and the entropy maximization [30]. In literature, this coupling is also called as metriplectic [31,32].…”

Section: A Note On the Geometric Foundations Of The 3d-qg Modelmentioning

confidence: 99%

On the nonlinear stability and the existence of selective decay states of 3D quasi‐geostrophic potential vorticity equation

Esen

Han

Şengül

et al. 2019

Math Methods in App Sciences

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In this article, we study the dynamics of large scale motion in atmosphere and ocean governed by the 3D-quasi-geostrophic potential vorticity (QGPV) equation with a constant stratification. It is shown that for a Kolmogorov forcing on the first energy shell, there exist a family of exact solutions which are dissipative Rossby waves. The nonlinear stability of these exact solutions are analyzed based on the assumptions on the growth rate of the forcing. In the absence of forcing, we show the existence of selective decay states for the 3D-QGPV equation. The selective decay states are the 3D-Rossby waves traveling horizontally at a constant speed. All these results can be regarded as the expansion of that of the 2D-QGPV system and in the case of 3D-QGPV system with isotropic viscosity. Finally, we present a geometric foundation for the model as a general equation for non-equilibrium reversible-irreversible coupling.

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Gradient Dynamics and Entropy Production Maximization

Cited by 13 publications

References 37 publications

Multiscale thermodynamics of charged mixtures

Multiscale thermodynamics of charged mixtures

Generalization of the dynamical lack-of-fit reduction

On the nonlinear stability and the existence of selective decay states of 3D quasi‐geostrophic potential vorticity equation

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