2nd Barcelona School
of Non-Equilibrium
Physics 

 Giulio Biroli: Generative AI and Diffusion Models: A Statistical Physics Perspective

Lecture 1 — Diffusion models, Langevin dynamics, and time-reversal.
Lecture 2 — Generation of data structure (“features”) and dynamical phase transitions.
Lecture 3 — Memorisation - Generalization transition: relationship with the Random Energy Model transition and dynamics in complex energy landscapes
Lecture 4 — (if time permits) Relationship between diffusion models and the Exact Renormalization Group.

Jean-Philippe Bouchaud: Out of Equilibrium Economics, Collective Effects & Crises

Lecture 1 — Equilibrium in physics vs economics; metastability, ergodicity breaking, slow dynamics and aging; RFIM and socio-economic applications; fragility, resilience and self-organized criticality.

Lecture 2 — Production functions; equilibrium in firm networks; analogies with Lotka–Volterra ecologies; non-equilibrium phase diagram (collapse, oscillations, chaos); instabilities and emergent inequalities.

Lecture 3 — Learning in complex worlds: rescuing rational equilibrium; learning, habit formation and ergodicity breaking; self-fulfilling prophecies and Kirman’s ants model.
Lecture 4 — Unlearnable games, satisficing equilibria, oscillations, aging and chaos; rewiring dynamics in firm networks.

 Florent Krzakala: Statistical Physics of Neural Networks: An introduction

Lecture 1 — Linear models, implicit regularization, and double descent; role of noise, initialization, and optimization bias; why bigger models may generalize better.

Lecture 2 — Two-layer networks: from lazy training to feature learning; transition from kernel behavior to genuine representation learning.

Lecture 3 — Scaling laws: performance scaling with data; evolution of the weight spectrum during training.
Lecture 4 — Toward multi-layer networks: hierarchical features, inter-layer correlations, and open theoretical challenges.

Valentina Ros: Out-of-Equilibrium Dynamics in High Dimensions — Fixed Points, Non-Reciprocity & Chaos

Lecture 1 — High-dimensional random systems: optimization dynamics, inference problems, and non-conservative interactions; applications to biological neural networks, generalized Lotka–Volterra models, and econophysics.

Lecture 2 — Random landscapes: counting minima; random-matrix tools; mean-field dynamics and aging; geometric interpretation of slow relaxation.

Lecture 3 — Dynamics without a landscape: non-reciprocal interactions; counting equilibria; dynamical mean-field theory; Lyapunov exponents and the relation between chaos and unstable equilibria.

Lecture 4 — Conclusions and perspectives: connections with examples and open problems.

 Marco Tarzia: Anderson Localization and Ergodicity Breaking

Lecture 1 — Physical origin of Anderson localization; tight-binding Hamiltonian; diagnostics (transport, spectral statistics, eigenstate properties); features of the Anderson transition and scaling ideas.

Lecture 2 — Quantum ergodicity and Many-Body Localization (MBL): ETH and its breakdown; phenomenology of MBL; mapping to Anderson localization on complex graphs.

Lecture 3 — Anderson localization on the Bethe lattice: Green’s functions, cavity method, analytical solution, phase diagram, and Ginzburg criterion.
Lecture 4 — Random matrix models for ergodicity breaking: Rosenzweig–Porter ensemble, phases, eigenvalue/eigenvector statistics, extensions and open problems.

Organisers