Introduction to the dynamics of disordered systems: equilibrium and gradient descent

TL;DR

This paper provides an introductory overview of the dynamics of disordered systems, focusing on equilibrium behavior, glass transition, and gradient descent dynamics, based on lecture notes from summer schools.

Contribution

It offers a pedagogical summary of disordered system dynamics, emphasizing equilibrium and off-equilibrium gradient descent, with selected topics tailored for educational purposes.

Findings

Overview of equilibrium dynamics and glass transition

Analysis of gradient descent in disordered systems

Selected topics illustrating key concepts

Abstract

This manuscript contains the lecture notes of the short courses given by one of us (F.Z.) at the summer school "Fundamental Problems in Statistical Physics XV", held in Brunico, Italy, in July 2021, and, just before that, at the summer school "Glassy Systems and Inter-Disciplinary Applications", held in Cargese, France, in June 2021. The course was a short introductory overview of the dynamics of disordered systems, focused in particular on the equilibrium dynamics (with the associated glass transition), and on the simplest case of off-equilibrium dynamics, namely the gradient descent dynamics. A few selected topics (and references) are chosen, based on the authors' own taste and competences, and on pedagogical reasons, without aiming at a complete review of the subject.