Statistical Physics

This course will reveal how the properties of materials and (living) systems are related to the physical properties of their components, and will offer methods to predict these properties.

These methods make use of the fundamental concepts of statistical physics, and will be applied to examples in materials science, food science and nanobiology.

The word "statistical" in this context should be related to "probability theory" and not so much to "statistics" (the mathematical discipline). Statistical physics uses a probabilistic approach to describe nature, and considers the properties of mesoscopic and macroscopic systems as expectation values, based on the stochastic behaviour of an underlying microscopic world of molecules or individual components (e.g. the collective behaviour of organisms in a group, polymers in an elastic tissue, iron atoms in a magnet, cars in traffic, etc.).

The concepts of microstates and macrostates will be introduced to offer a new definition of Entropy, the Boltzmann entropy (and connected, the Gibbs entropy / Shannon entropy) that puts entropy on a clear and quantitative microscopic basis. This course connects Mechanics (of particles) with Thermodynamics (of systems, fluids) using the Boltzmann entropy and the fundamental law of statistical physics, and it even 'derives' the second law of thermodynamics.

Thermodynamics is shortly revised, and in particular, thermodynamic processes, and the aspect that the work performed on a system depends on what thermodynamic variables are controlled. This amount of work corresponds to a change in a thermodynamic potential (the energy, the Helmholtz free energy, the Gibbs free energy, etc.). Later in the course, this potential will be derived from the microscopic properties of the system, using statistical physics, and in particular, the Boltzmann distribution.

In the second half of the course, many applications of the theory will be discussed: why systems can undergo 'phase transitions' or separate into multiple coexisting phases, why polymers are elastic, why adding salt to a recipe may influence the cooking process, what a critical point is, and potential driving mechanisms behind the self-organisation of proteins into temporal membrane-less clusters.

And much more...