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Nonequilibrium Field Theories and Stochastic Dynamics

These are self-study notes for the course Nonequilibrium Field Theories and Stochastic Dynamics (Prof. Erwin Frey, LMU Munich, Summer Semester 2025). Prof. Erwin Frey prefers chalkboard lectures. To document my learning, I organized my notes into articles and wrote Python code to deepen understanding.

Course link: https://www.youtube.com/watch?v=-pEPKnuN1iY&list=PL2IEUF-u3gRdSbgtuqH5RNTuT798s0GqX

Note: I followed the course on YouTube only; there is no official handout. Everything here comes from notes taken while watching the videos. A sample of the original notes is below:

Personal notes sample

Course Playlist: YouTube Playlist

Official Course Link: LMU Munich - Nonequilibrium Field Theories and Stochastic Dynamics

Course Outline

Course Outline

Course Contents

This lecture series explores the fundamental principles and advanced concepts of nonequilibrium field theories and stochastic dynamics. The course focuses on stochastic processes in particle and field systems, emphasizing mathematical formalisms such as Langevin equations, Fokker-Planck equations, and path integrals. Additionally, the lectures cover applications in soft matter physics, active matter, and non-equilibrium statistical mechanics.

The notes consist of four parts, totaling forty lectures:

Part I: Foundations of Stochastic Processes. From random walks and Brownian motion (Bernoulli or Gaussian walks; diffusion equation) through elementary stochastic models (Poisson processes, birth-death dynamics, molecular motors) to Markov processes and master equations (Chapman-Kolmogorov; discrete and continuous state spaces).

Part II: Stochastic Dynamics of Particles. Langevin and Fokker-Planck equations (path integrals; multiplicative noise), stochastic simulation (Gillespie algorithm; stochastic integration), and stochastic thermodynamics (entropy production, detailed balance, fluctuation theorems).

Part III: From Discrete States to Fields. Reaction networks to field theories via the master equation and Kramers-Moyal expansion; coarse-grained field dynamics (relaxational dynamics; conserved vs. non-conserved fields).

Part IV: Field Theories of Nonequilibrium Systems. Dynamical functionals and MSR formalism (Onsager-Machlup; Janssen-de Dominicis), fluctuating hydrodynamics and Model H, nonequilibrium pattern formation, and active-matter field theory.

Usage

Each Python file corresponds to specific topics covered in the lecture series. The code serves as practical implementations of the theoretical concepts presented in the YouTube videos, developed as part of self-study and learning notes.

Here are some code output demonstrations:

code/5.PhaseDiagram.py

code/13.MCMC_LotkaVolterra.py

code/16.MIPS.py

code/19.OverdampedLangevinEquation.py

code/26.CriticalSlowingDown1.py

code/27.ScalarField.py

code/28.VortexDecayDemo.py

code/30.AdvectionAndDiffusion.py

code/35.Schlöglmodel.py

code/37.PercolationFieldTheory.py

code/38.Rock-Paper-Scissors.py

code/39.ReactionFront.py

code/40.InertialSpin.py

Prerequisites

  • Statistical mechanics and thermodynamics
  • Probability theory and stochastic processes
  • Differential equations
  • Basic knowledge of field theory (helpful but not required)

License

This project is licensed under the CC BY-NC-ND 4.0 License.

Acknowledgments

  • Prof. Erwin Frey and the Physics of Life group at LMU Munich for the excellent lecture series
  • PhysicsOfLifeLMU YouTube Channel for making these lectures publicly available

Citation

If you find this repository useful, you may cite it in BibTeX format:

@misc{liu2025nonequilibrium,
  author = {Liu, Zhihang},
  title = {Nonequilibrium Field Theories and Stochastic Dynamics: Course Notes and Code},
  year = {2025},
  url = {https://github.com/Liu-Zhihang/Nonequilibrium-Field-Theories-and-Stochastic-Dynamics},
  note = {Self-study notes for the course by Prof. Erwin Frey, LMU Munich}
}