Nonequilibrium thermodynamics and statistics - an introduction

NOTE: The date and time for the exercises will be discussed in the first lecture

Contents:

We will give an introduction to non-equilibrium physics, both on the macroscopic (thermodynamic) and the microscopic (kinetic) level.

We will start by generalizing equilibrium thermodynamics to spatial degrees of freedom. By allowing for small currents (of heat or particles, for instance), the theory of linearly irreversible thermodynamics will be developed. A major insight will be the occurrence of cross-coupling effects, like the Peltier and Soret effect, obeying important symmetries (Onsager relations, Nobel Prize in Chemistry 1968). The occurrence of instabilities (I. Prigogine, Nobel Prize in Chemistry 1977) will also be discussed.

We will then switch to the microscopic scale and motivate the famous Boltzmann equation, the foundation of transport theory. We will solve it by several approximation methods and use it to derive macroscopic balance equations, yielding a microscopic foundation of the processes described in the first part of the lecture.

Finally, we make a close connection to equilibrium statistical physics, by discussing linear response theory and deriving the fluctuation-dissipation theorem. The main insight will be that the response of a system to a small perturbation, i.e. the outcome of a non-equilibrium situation, can be calculated within equilibrium theory.

If time permits, at the end we will discuss few current research topics, like the use of Boltzmann-type equations in the modeling of 'active' systems (collective motion of animals, dynamics of cellular extracts) and the occurrence of nonequilibrium phase transitions in boundary-driven transport (asymmetric exclusion processes).

Criteria for certificate: ungraded: 50% of exercise points ; graded: 50% of exercise points + oral exam