Lectures by Christian Maes
Title: Linear response theory
Introductory: What is nonequilibrium?
Relevant papers
1) Aaron Beyen, Faezeh Khodabandehlou and Christian Maes, Quasistatic response for nonequilibrium processes: evaluating the Berry potential and curvature. Journal of Physics A: Mathematical and Theoretical 59, 205001 (2026).
2) Lander Bogers, Faezeh Khodabandehlou and Christian Maes, Negative specific heats: where Clausius and Boltzmann entropies separate. Physical Chemistry Chemical Physics 27, 15009-15023 (2025).
3) Christian Maes, Response theory: a trajectory-based approach. Frontiers in Physics, section Interdisciplinary Physics (2020).
4) Christian Maes and Maarten H. van Wieren: Time-symmetric fluctuations in nonequilibrium systems , Physical Review Letters 96, 240601 (2006).
Lectures by Dibyendu Das:
Title: Stochastic Processes related to Gene Expression and Cell Division
Lecture-1: Number fluctuations & first passage in cell populations.
Cell age-distribution in a growing population.
Lecture-2: Stochastic gene expression: Fluctuations and threshold crossing (first passage) of gene products
Lecture-3: Distribution of mRNA threshold crossing times in Laplace space.
Lecture-4: Distribution of protein threshold crossing times in Laplace space;
application to experiments on cell lysis & pore formation in endosomes.
Lecture-5: Heterogeneity in cell division times (first passage times) —>impact on distribution of protein count in cellular ensembles.
Relevant reading material: https://drive.google.com/drive/folders/1p2v_l-Fb1NrMFhDLyQseQo-IVSPWEv7c?usp=drive_link
Lectures by Hugo Touchette:
Title: Introduction to reinforcement learning
Preparation lecture 0: Markov processes (On YouTube)
Lecture 1: Markov reward processes
Lecture 2: Markov decision processes
Lecture 3: Optimal equations and Bellman equations
Lecture 4: Dynamic programming
Lecture 5: Temporal difference methods
Relevant Videos and Reading material: https://www.youtube.com/watch?v=I3V-NULa1no
For material to read: R. S. Sutton and A. G. Barto. Reinforcement Learning: An Introduction, MIT Press, Cambridge, MA, 2nd ed. edition, 2018.
Available for free at http://incompleteideas.net/book/the-book-2nd.html
Material for Tutorials: pdf1, pdf2, pdf3, pdf4
Lecture Notes: pdf
Lectures by Valentina Ross:
Title: Out-of-equilibrium in high-dimensional systems with disorder
In these lectures, I will discuss the dynamics of high-dimensional complex systems, namely systems composed of many interacting degrees of freedom coupled through random all-to-all interactions that may be non-reciprocal. I will focus on models whose dynamics is analytically tractable, at least to some extent, and I will discuss the types of out-of-equilibrium behavior they generate (such as aging and chaos) and how these phenomena are affected by high dimensionality and non-reciprocity.
Lecture 1. Introduction: setting, questions, and roadmap. Simple models with non-reciprocal interactions: linear random forces and non-linear random forces.
Lecture 2. Warm-up: finite-N systems with linear random forces. Concepts: relaxation dynamics, landscapes, equilibrium and non-equilibrium behavior. Tools: mode decomposition and ordinary differential equations.
Lecture 3. Large-N systems with linear forces: averaging over initial conditions; spectral properties of large asymmetric random matrices and their impact on the dynamics.
Concepts: concentration, self-averaging, and universality.
Tools: random matrix theory.
Lecture 4. Large-N systems with linear forces: asymptotically long-time dynamics; slow relaxation; effect of non-reciprocity. Concepts: separation of time scales, aging, slow (algebraic) decay, and acceleration induced by non-reciprocity. Tools:large-N asymptotic analysis.
Lecture 5. Large-N systems with non-linear forces: dynamical mean-field theory (DMFT) and chaos in high dimensions. Concepts: mean-field dynamics, self-consistent stochastic processes, fixed points versus chaotic dynamics. Tools: DMFT equations and their asymptotic analysis, Hamiltonian formulation, Kac–Rice formalism (just a few words if time permits).
Lecture Notes: pdf