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Redukce v nerovnovážné termodynamice
Thesis title in Czech: Redukce v nerovnovážné termodynamice
Thesis title in English: Reductions in non-equilibrium thermodynamics
Key words: Nerovnovážná termodynamika, GENERIC, Chapman-Enskog, Ehrenfest, redukce
English key words: Non-equilibrium thermodynamics, GENERIC, Chapman-Enskog, Ehrenfest, reduction
Academic year of topic announcement: 2018/2019
Type of assignment: dissertation
Thesis language:
Department: Mathematical Institute of Charles University (32-MUUK)
Supervisor: RNDr. Michal Pavelka, Ph.D.
1) Review of the GENERIC framework
2) Formulation of the Chapman-Enskog reduction within the framework
3) Formulation of the Ehrenfest reduction within the framework
4) Application to some particular reductions, e.g. reduction of kinetic theory to fluid dynamics including turbulence
Grmela, Öttinger, Dynamics and thermodynamics of complex fluids. I. Development of a general formalism, Phys. Rev. E (1997), vol. 56(6)
Öttinger, Grmela, Dynamics and thermodynamics of complex fluids. II. Illustrations of a general formalism Phys. Rev. E (1997), vol. 56(6)
Gorban, Basic types of coarse-graining,
Preliminary scope of work in English
Non-equilibrium thermodynamics it a bunch of physical theories that should provide evolution equations of any physical processes observed on macroscopic and mesoscopic scales. Indeed, Hamilton canonical equations (Newton laws) and equilibrium thermodynamics are part of nowadays non-equilibrium thermodynamics as well as any mesoscopic level of description between them (kinetic theory, fluid dynamics, dynamics of solids, viscoelastic fluids, etc.). The holy grail of non-equilibrium thermodynamics is to find a general and feasible reduction method producing less detailed descriptions from more detailed in a systematic way.

Reductions like Chapman-Enskog method, Ehrenfest method or projection operators have successfully been applied to particular systems. However, none of them can be characterized as feasible, general and systematic at once. On the other hand, many evolution equations describing physically relevant systems have been shown to have the GENERIC structure, where reversible dynamics is given by a Hamiltonian structure while the irreversible by a dissipation potential. If one has a GENERIC structure, how does the Chapman-Enskog and Ehrenfest method reduce it? Is the GENERIC structure preserved by the reduction? The goal of this thesis is to answer that questions and to generalize and simplify the reduction methods by formulating them geometrically.
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