GENERIC guide to the multiscale dynamics and thermodynamics

Grmela, Miroslav

doi:10.1088/2399-6528/aab642

Cited by 55 publications

(35 citation statements)

References 81 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Emergence of various entropies in the analysis of the time evolution of both externally unforced and driven systems has already been discussed in [16], [18]. In this paper we have worked out a simple illustration.…”

Section: Discussionmentioning

confidence: 91%

Entropy and Entropy Production in Multiscale Dynamics

Grmela

Pavelka

Klika

et al. 2019

Journal of Non-Equilibrium Thermodynamics

Self Cite

View full text Add to dashboard Cite

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 equilibrium or the final stage in the investigation of the approach from the Cattaneo level. Both investigations bring to the Fourier level an entropy and a thermodynamics. In the absence of external and internal influences preventing the approach to equilibrium the entropy that arises in the latter investigation is the production of the classical entropy that arises in the former investigation. If the approach to equilibrium is prevented, then the entropy that arises in the investigation of the approach from the Cattaneo level to the Fourier level still brings to the Fourier level the entropy and the thermodynamics even if the classical entropy and the classical thermodynamics is absent. We also note that vanishing total entropy production as a characterization of equilibrium state is insufficient.

show abstract

Section: Discussionmentioning

confidence: 91%

Entropy and Entropy Production in Multiscale Dynamics

Grmela

Pavelka

Klika

et al. 2019

Journal of Non-Equilibrium Thermodynamics

Self Cite

View full text Add to dashboard Cite

show abstract

“…In general, the passage from more detailed to less detailed levels of description requires an entropy accounting for the eliminated degrees of freedom and leads to the emergence of irreversibility [29]. Also for irreversible systems, the consideration of the combined space is a powerful tool for elaborating the relation between two levels of description [30][31][32][33][34]. A detailed comparison of the ideas for irreversible systems with the construction of composite reversible theories proposed in the present work might be illuminating.…”

Section: Discussionmentioning

confidence: 85%

Natural Hamiltonian formulation of composite higher derivative theories

Öttinger

2019

J. Phys. Commun.

View full text Add to dashboard Cite

If a higher derivative theory arises from a transformation of variables that involves time derivatives, a tailor-made Hamiltonian formulation is shown to exist. The details and advantages of this elegant Hamiltonian formulation, which differs from the usual Ostrogradsky approach to higher derivative theories, are elaborated for mechanical systems and illustrated for simple examples. Both a canonical space and a set of constraints emerge naturally from the transformation rule for the variables. In other words, the setting for quantization and the procedure for eliminating instabilities arise naturally.

show abstract

“…In eq. 2, the dissipation potential Ψ * is a convex real-valued function of ξ that has its minimum at 0, where Ψ * (x, 0) = 0 (for the origins of using dissipation potentials in irreversible thermodynamics, see [28,29,30,31,32]; see also the remarks in Section 2.9 of [33]). The potential Ψ * can have an additional explicit dependence on x.…”

Section: A Framework For Nonequilibrium Thermodynamicsmentioning

confidence: 99%

A Framework of Nonequilibrium Statistical Mechanics. I. Role and Types of Fluctuations

Öttinger

Peletier

Montefusco³

2020

Journal of Non-Equilibrium Thermodynamics

View full text Add to dashboard Cite

Understanding the fluctuations by which phenomenological evolution equations with thermodynamic structure can be enhanced is the key to a general framework of nonequilibrium statistical mechanics. These fluctuations provide an idealized representation of microscopic details. We consider fluctuation-enhanced equations associated with Markov processes and elaborate the general recipes for evaluating dynamic material properties, which characterize force-flux constitutive laws, by statistical mechanics. Markov processes with continuous trajectories are conveniently characterized by stochastic differential equations and lead to Green–Kubo-type formulas for dynamic material properties. Markov processes with discontinuous jumps include transitions over energy barriers with the rates calculated by Kramers. We describe a unified approach to Markovian fluctuations and demonstrate how the appropriate type of fluctuations (continuous versus discontinuous) is reflected in the mathematical structure of the phenomenological equations.

show abstract

GENERIC guide to the multiscale dynamics and thermodynamics

Cited by 55 publications

References 81 publications

Entropy and Entropy Production in Multiscale Dynamics

Entropy and Entropy Production in Multiscale Dynamics

Natural Hamiltonian formulation of composite higher derivative theories

A Framework of Nonequilibrium Statistical Mechanics. I. Role and Types of Fluctuations

Contact Info

Product

Resources

About