# Advanced Statistical Physics and new applications

Statistical physics is witnessing a revolution : understanding the dynamics of a very large number of interactive degrees of freedom, which has been from the beginning the main aim of statistical physics, has become now a central problem in many fields such as physics, biology, computer science, just to cite a few.

Now more than ever, statistical physics is both for its methods and its applications a very powerful discipline with a very broad range of theoretical methods and ramifications in many branches of science.

The aim of this series of lectures is facing the students with this very rich state of the art :

on one hand by teaching fundamental notions and methods of statistical physics and at the same time by presenting its modern applications in physics and beyond.

- Statistical Dynamics
- Sochastic Processes
- Time-reversal and its consequences
- Metastability and rare-events
- The mean-field approximation
- Exactly solvable models
- Critical dynamics and mesoscopic descriptions

**Concepts and techniques to be revised before the beginning of the first semester** :

Equilibrium statistical physics : statistical ensembles, thermodynamics, basic notions of phase transitions.

Students should have a good knowledge of statistical ensembles (canonical, micro-canonical and grand-canonical) and their use to compute thermodynamic properties of equilibrium systems.

Basic notions and examples of phase transitions are also required.

To have a concrete idea of the material requested, students can browse the

Kerson Huang’s book on "Statistical Mechanics" Chaps 1,2,6,7,8.

Students can use their favourite book to revise.

Mathematical tools : basic probability theory, operator formalism.

A good working knowledge of basic probability theory will be important, in particular probability measures, conditioned probability, averages and moments.

The basic working knowledge on operator formalism used for quantum mechanics will be also required (functional operator, eigenstates, eigenvalues, etc).

The undergraduate texts the students had already used on these topics will be enough to revise.

Beyond that, students should be familiar with Fourier transforms and Gaussian integrals.

A non-exhaustive list of possible sources from which one can choose :

- Physique Statistique, G. Roux et C. Texier
- Physique Statistique, N. Pavloff at N. Sator
- G. Montambaux, https://www.equipes.lps.u psud.fr/Montambaux/polytechnique/PHY433/poly-PHY433-2017.pdf
- Statistical Physics of Particles, M. Kardar
- Statistical Mechanics, Order Parameters and Complexity, J. P. Sethna
- Principles of condensed matter physics, P. Chaikin, T. LubenskyStatistical Mechanics, K. Huang