Statistical physics - 4PMNPHS9

Goal(s)

The aim of this course is to go beyond equilibrium statistical physics and to explore how statistical physics concepts can be extended to out-of-equilibrium systems and to particles in interaction.

We will start with out-of-equilibrium systems, such as often met in experiments in fundamental and applied physics. We will explore the physical origin and theoretical treatments of irreversibility, for instance during the evolution of gases and fluids. We will also relate our approach to the thermodynamic theory of irreversible processes.

In a second part, we will address Brownian motion at the basis of the theory of diffusion, which has currently many applications in biology.

Finally, we will address particles in interaction, such as involved in nanomagnetism. We will see that their study often requires a numerical approach and will discuss one of them, namely the Monte Carlo method.

Content(s)

Chapter I - Out-of-equilibrium systems : Master equation, detailed balance, H theorem

Chapter II - Out-of-equilibrium systems : Boltzmann equation : derivation, conservation equation, link with thermodynamic theory of irreversible processes, Onsager realtions, transport phenomena

Chapter III - Brownian motion : random walker, Langevin model, fluctuation-dissipation theorem, applications in biology

Chapter IV - Systems in interaction : Ising model, ferromagnetism, mean field, transfert matrix, Monte Carlo method