84 citations · 319 across the 26 of their papers we have counts for
12 papers · 1 filter
Comparison of some geometric frameworks for dissipative evolution in multiscale non-equilibrium thermodynamics
Miroslav Grmela, Michal Pavelka
In this paper, we review and compare some geometric frameworks for dissipation in non-equilibrium thermodynamics. We start with a brief overview of classical irreversible thermodyn…
Classical and Multiscale Non-equilibrium Thermodynamics
Miroslav Grmela, Michal Pavelka
Classical and multiscale non-equilibrium thermodynamics have different histories and different objectives. In this Note we explain the differences and review some topics in which t…
Multiscale Theory
Miroslav Grmela
Boltzmann kinetic equation is put into the form of an abstract time evolution equation representing links connecting autonomous mesoscopic dynamical theories involving varying amou…
On the role of geometry in statistical mechanics and thermodynamics II: Thermodynamic perspective
Ogul Esen, Miroslav Grmela, Michal Pavelka
The General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) provides structure of mesoscopic multiscale dynamics that guarantees emergence of equilibrium st…
On the role of geometry in statistical mechanics and thermodynamics I: Geometric perspective
Ogul Esen, Miroslav Grmela, Michal Pavelka
This paper contains a fully geometric formulation of the General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC). Although GENERIC, which is the sum of Hami…
Multiscale Thermodynamics
Miroslav Grmela
Multiscale thermodynamics is a theory of relations among levels of investigation of complex systems. It includes the classical equilibrium thermodynamics as a special case but it i…
Generalization of the dynamical lack-of-fit reduction
Michal Pavelka, Vaclav Klika, Miroslav Grmela
The lack-of-fit statistical reduction, developed and formulated first by Bruce Turkington, is a general method taking Liouville equation for probability density (detailed level) an…
Entropy and Entropy Production in Multiscale Dynamics
Miroslav Grmela, Michal Pavelka, Vaclav Klika +2
Heat conduction is investigated on three levels: equilibrium, Fourier, and Cattaneo. The Fourier level is either the point of departure for investigating the approach to equilibriu…
Landau damping in the multiscale Vlasov theory
Miroslav Grmela, Michal Pavelka
Vlasov kinetic theory is extended by adopting an extra one particle distribution function as an additional state variable characterizing the micro-turbulence internal structure. Th…
Hamiltonian and Godunov Structures of the Grad Hierarchy
Miroslav Grmela, Liu Hong, David Jou +2
The time evolution governed by the Boltzmann kinetic equation is compatible with mechanics and thermodynamics. The former compatibility is mathematically expressed in the Hamiltoni…
Externally driven macroscopic systems: Dynamics versus Thermodynamics
Miroslav Grmela
Experience collected in mesoscopic dynamic modeling of externally driven systems indicates absence of potentials that could play role of equilibrium or nonequilibrium thermodynamic…
Boundary layer variational principles: A case study
Miroslav Grmela, Iliya V. Karlin, Vladimir B. Zmievski
Considering the model heat conduction problem in the setting of Grad's moment equations, we demonstrate a crossover in the structure of minima of the entropy production within the…