Collective processes in non-equilibrium systems

Collective processes in non-equilibrium systems (winter term 2020/21)

Steffen Rulands

Time: Starting on Nov 3, Tuesdays, 4:40pm CET


Online via Zoom (link)

Limited physical attendance if regulations allow:

Seminar Room 3
Max Planck Institute for the Physics of Complex Systems
Noethnitzer Str. 38
01187 Dresden

Summary: Suppose someone gave you a terabyte of data on an epidemic. What are the theoretical concepts you need to know in order to understand collective behaviour in such a system? Technological breakthroughs in biology and the social sciences now give unprecedented access to microscopic states of non-equilibrium systems, requiring a rethinking about our approaches to understanding collective degrees of freedom in complex systems. In this lecture, we will take an interdisciplinary perspective on the concepts necessary to identify and understand collective order in space and time. We will begin by introducing core concepts from non-equilibrium statistical physics, such as stochastic processes, field theory, renormalisation group theory and non-equilibrium phase transitions, and complement these tools with approaches from data science and machine learning that allow identifying collective degrees of freedom in high-dimensional measurements. We will synthesise these lessons using examples from current research.

Required prior knowledge: Statistical physics

Course materials

Password for PDF files is the last name of the lecturer.

Overview over the lecture - collective non-equilibrium processes - fluctuation-dissipation theorem

Lecture notes (PDF)

Stochastic processes - Stochastic differential equations - Master equations - Fokker-Planck equations

Lecture notes (PDF)

Non-equilibrium field theory - Path integral representation of the Langevin equation - Path integral representation of spatially extended Langevin system

Lecture notes (PDF)

How order is established in non-equilibrium systems - Peierl's argument - Mermin-Wagner theorem - Polar order in the Viscek model

Lecture notes (PDF)

Transitions between non-equilibrium steady states in the absence of noise - homogeneous nonlinear dynamical systems - bifurcations - spatial structures - linear instability

Lecture notes (PDF)

Equilibrium criticality - scaling laws - fluctuations in epidemic spreading - non-equilibrium criticality

Lectures notes (PDF)

Introduction to renormalisation group theory

Lectures notes (PDF)

Renormalisation of an epidemic model

Lectures notes (PDF)

Dimensionality reduction and clustering

Data visualisation using ggplot2 - data science project example

Slides data visualisation (PDF)

Code (GitHub)

Practical example: scaling of epigenetic patterns in embryo developments