Thermodynamics of irreversible phenomena.

• Elaboration of a general theoretical framework of irreversible phenomena having as starting points the kinetic theory of gases and classical thermodynamics
• Presentation of the classical theory of Onsager-Prigogine. Presentation of more recent theories such as Rational Thermodynamics (theory of Truesdell & Noll) and Extended Thermodynamics (theories of Jou & Lebon and of Müller).

1. Summary of equilibrium thermodynamics: first thermodynamic axiom (principle of energy conservation), absolute temperature and entropy, second thermodynamic axiom, Gibbs relation, equations of Euler & Duhem, thermodynamic potentials and Legendre transformations, stability of equilibrium states, evolution principles, thermochemistry.
2. Classical theory of irreversible thermodynamics (theory of Eckart-Onsager-Prigogine): local equilibrium, balance laws and constitutive relations, entropy production, thermodynamic fluxes and forces, Onsager-Casimir reciprocal relations. Applications: Fourier-Navier-Stokes equations for Newtonian fluids, thermodiffusion.
3. Study of thermo-electric phenomena: Hall effect, Seebeck and Peltier effects, Nerst and Ettinghausen effects, Joule and Thomson heats.
4. Kinetic theory of gases. Derivation of the Boltzmann equation. Collision operator. Relations between mascroscopic variables and kinetic theory. H-theorem. Collision invariants, Maxwell-Boltzmann distribution and derivation of balance laws. Justification of local equilibrium hypothesis. Theory of fluctuations of Einstein.  Derivation of the Onsager-Casimir reciprocal relations.
5. Introduction to rational thermodynamics. material memory, objectivity, Clasius-Duhem inequality, material-frame indifference, constitutive relations.  Application in thermo-elastic materials, comparison with the linear theory of Eckart-Onsager-Prigogine. Liu's method of Lagrange multipliers and extended theories.
6. Stationary states: criteria for minimum of entropy production and minimum of dissipated energy. Introduction to stability theory. Rayleigh-Bénard instability.

Due to the COVID-19 crisis, the information in this section is particularly likely to change.

• Course lectures
• Sessions of exercises
• Lectures in the classroom or mixed (classrooms with simultaneous broadcasting on Teams) depending on the pandemic conditions

Due to the COVID-19 crisis, the information in this section is particularly likely to change.

•     Written exam, with open books and notes. The score on the exam counts for 70% of the overall score (grade) on the course.
•     3 homework assignments. The score on each assignment counts for 10% of the overall score (grade) on the course.
•    We maintain the right to ask a student for an oral exam in case of technical problems or suspicion of fraude.

• G. Lebon, D. Jou & J. Casas-Vasquez, Understanding Non-equilibrium Thermodynamics, Springer, 2008.  Mandatory, available on the e-books of the library in electronic form.
• D. Kondepudi & I. Prigogine, Modern Thermodynamics, Wiley, 1999. Recommended.
• S.R. De Groot  and P. Mazur, Non-equilibrium Thermodynamics, Dover,  1984. Recommended.

• M.V Papalexandris, Thermodynamics of Irreversible Phenomena, 2020. Hand-written notes, available on the moodle site of the course.
• Homework assignments, available on the moodle site of the course.