PHYSICS OF COMPLEX SYSTEMS

Introduction to the physics of complexity and of emergent phenomena (general points of view of P.W. Anderson, N. Goldenfeld, L.P. Kadanoff, ...)

Brief overview of Brownian motion, stochastic differential equations and stochastic processes.
Statistical mechanics out of equilibrium: microscopic reversibility and macroscopic irreversibility.
Detailed balance in equilibrium. Linear response theory and transport phenomena.
Onsager reciprocity relations with examples (Seebeck and Peltier effects, etc.)
Fluctuation-response theorem, dynamic susceptibility and fluctuation-dissipation theorem. Kramers-Kronig relations. Microscopic basis of Brownian motion.

Thermodynamics out of equilibrium at the micro- and nano-scales. Markovian description of non-equilibrium dynamics. Fluctuation theorems and work identities. Generalized detailed balance. Entropy production.

Out-of-equilibrium phase transitions. Directed percolation. Asymmetric simple exclusion and
related processes, some basic results. Theory of large deviations. Molecular motors. Applications of Gallavotti-Cohen theorem.

Stochastic dynamics of surfaces and interfaces: the Kardar-Parisi-Zhang equation.

Computational complexity and information theory. The random energy model and the random code ensemble. Complex energy landscapes and reweighting methods.