Non-equilibrium Thermodynamics

Both the Fokker-Planck and Langevin equations describe the Brownian motion. In general, they also explain the behavior of a system in presence of a random noise and its evolution toward a stationary state i.e., they could also be applied to thermalization processes of non-equilibrium systems.

Text and Reference Books

Some texts, online or otherwise are given below:

  • Linda Reichl: A Course in Modern Statistical Physics.
    • Chapter 7 is about Brownian Motion and Fluctuation Dissipation
  • Kerson Huang: Introduction to Statistical Physics
    • See chapter 14
  • Bikkin, Lyapilin: Non-equilibrium thermodynamics and physical kinetics
  • Attard: Non-Equilibrium Thermodynamics and Statistical Mechanics
  • Balakrishnan:
  • Pottier: Non-Equilibrium Statistical Physics
  • Ropke: Non-Equilibrium Statistical Physics
  • Peliti & Pigolotti: Stochastic Thermodynamics
    • See Chapter 4: Jarzynski and Crooks relations
  • Banerjee: Open Quantum Systems

Other texts

  • Woyczyński - Diffusion Processes, Jump Processes, and Stochastic Differential Equations
  • David Tong: Lectures on Kinetic Theory
  • Kardar: Statistical Theory of Particles

Topics (Subject to change)

Brownian Motion

Langevin, Fokker-Planck, Master Equation:

  • Balakrishnan (Chapters 1-6)
  • Zwanzig (Chapters 1-3)
  • Banerjee: Open Quantum Systems (Chapter 3)

Transport Phenomena/Boltzmann Equation

  • Marder, Condensed Matter Physics, Chapter 17.
  • Link

BBKGY Hierarchy - Kremer: An Introduction to the Boltzmann Equation and Transport Processes in Gases

Open Quantum Systems

  • H theorem
  • GKLS Equations
  • Open quantum systems

Langevin equation
Fokker Planck equation
Linear Response Theory

Progression

Week 1-2

Strand A: Stochastic thermodynamics

We will develop the Langevin and Fokker Planck Equations. Ultimately we will head towards the GSKL equations following Banerjee. Specifically you might hear:

  • Langevin Equation
  • Fokker Planck Equation
  • Liouville theorem
  • Smoluchowski equation
  • Kramers Moyal expansion

Texts:

  • Balakrishnan (Chapters 1-6)
  • Zwanzig (Chapters 1-3)
  • Banerjee: Open Quantum Systems (Chapter 3)

Week 3

Strand B: Transport phenomena

In tandem we will develop the Boltzmann equation. Some concepts:

  • Boltzmann equation
  • Relaxation time approximation.

Texts:

  • Marder, Condensed Matter Physics (Chapter 17)
  • Link

Week 4-6

Brownian Motion & Diffusion

Week 7-8

Boltzmann Equation and H-theorem

BBKGY Hierarchy - Kremer: An Introduction to the Boltzmann Equation and Transport Processes in Gases

Week 9+

SDEs

Week 10+

Jarzynski, Crooks?