# Gentlemen's Club of Non-equilibrium Thermodynamics

The seminar was held in autumn semester 2014

## Sessions

• ### Fundamental concepts in non-equilibrium thermodynamics (14.10.2014-MP)

What is non-equilibrium thermodynamics. Different levels of description. Kac ring. Reversibility/irreversibility. Entropy.
• ### Reversible dynamics (21.10.2014-MP)

General form of GENERIC - the reversible part. Poisson brackets. Reversibility. Degeneracy. Poisson bracket in Hamiltonian dynamics.

• ### Irreversible dynamics (4.11.2014 - MP)

Irreversible evolution within GENERIC. Dissipation potential and dissipative bracket. Heat equation.
• ### Classical hydrodynamics (11.11.2014 - MP)

Reversible evolution. Poisson bracket. Energetic and entropic formulation.
• ### Classical hydrodynamics (18.11.2014 - VK)

Irreversible evolution in classical hydrodynamics. Navier-Stokes-Fourier.
• ### Ir/reversibility revisited (25.11.2014 - MP)

Finishing the irreversible part of Navier-Stokes-Fourier. Maxwell-Cattaneo's equation. Checking ir/reversibility of Fourier, Navier-Stokes-Fourier and Maxwell-Cattaneo. GENERIC near equilibrium. Onsager-Casimir reciprocal relations.
• ### Boltzmann equation (2.12.2014 - MP)

GENERIC formulation. Ir/revesibility. Appetizer for differential geometry.
• ### Geometric formulation (9.12.2014 - MP)

Vector fields in differential geometry. Is the reversible part of Boltzmann equation really reversible? To show it we need a geometric formulation of ir/revesibility because the distribution function has no parity. How to derive the hydrodynamic Poisson bracket. Poisson bracket for mixtures of fluids. Maybe polymeric fluids.
• ### Poisson bracket (16.12.2014 - MP)

Derivation of the hydrodynamic Poisson from the Boltzmann Poisson bracket, derivation of the Boltzmann Poisson bracket from the Liouville Poisson bracket. Derivation of the Poisson bracket of binary mixtures.
• ### Summary (6.1.2015 - MP)

Summary of the seminar. A recipe for preparing a GENERIC model.
Gentlemen's club 2013/2014.
MP = Michal Pavelka, VK = Václav Klika

## Some nice books and papers

• 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)
• Jou, Casas-Vázquez, Lebon: Understanding Non-equilibrium Thermodynamics
• Öttinger, H. C., Constraints in nonequilibrium thermodynamics: General framework and application to multicomponent diffusion, J. Chem. Phys (2009), 130(11)
• Salmon, R., Hamiltonian fluid mechanics, Ann. Rev. Fluid Mech. (1988), 20
• Fecko, M., Differential Geometry and Lie Groups for Physicists, CUP 2006
• Lebon, Jou, Casas-Vázquez: Extended Non-Equilibrium Thermodynamics
• Öttinger: Beyond Equilibrium Thermodynamics
• Callen: Thermodynamics and an Introduction to Thermostatistics
• Atkins, de Paula: Atkins' Physical Chemistry