2020 04 12 I provide now a first draft of a skript with exercises in Sage
that are packed with the skript in a gzip-compressed tar bundle.
2020 04 07 Rather than with lectures we will start the course on Stochastic Processes by a software project
where we develop a suite of numerical tool to simulate stochastic processes and display the results.
This page is the opening call for the project. Please contact me if you are interested to participate.
Probabilities. distributions, moments, cumulants
characteristic functions, Laplace-Legendre transformations
Random Processes. random walks, Lévy walks, anomalous transport
central limit theorem, Lévy distribution, large deviation theory
Markov processes. master equation, Kramers-Moyal expansion, Fokker-Planck equation
ergodicity, transport theory, first passage problems
Langevin dynamics. stochastic differential equations, Stratonovic and Ito calculus
Kramers problem, reactions coordinates, path of least action
stochastic thermodynamics, fluctuation relations, linear-response theory
Stochastic Thermodynamics. fluctuation relations, thermodynamic efficiency, linear-response theory
I will use Python and Sage for numerical studies and visualization. The script files are notebooks that run interactively in Jupyter. Please store them on your computer, start Jupyter, and then open the notebook. The files contain fairly minimalistic explanations and comments. Feel free to add more comments and explanations, and return them to me.
As introductions to Python and Sage I recommend the books Steward: "Python for Scientists" and Zimmermann u.a.: "Computational Mathematics with SageMath".
I am working on a skript with more information on the course. The PDF-version of the first draft can be downloaded here. A gzip-compressed tar bundle that contains the PDF-file and Sage-Skripts with further illustrations and first homework assignments is available here.
Set   Topic Assignment 00. Foundations study Sect. 1–2 of J. L. Garcia-Palacios: Intro to the theory of stoch processes and Brownian motion, arXiv:cond-mat/0701242 » 01. Probabilities study Chapter 1 of my lecture notes and complete the open tasks in the Sage-files provided in this bundle. 02. Probability Distributions study Chapter 2 of Haken’s book and complete the tasks of exercise set 2. 03. Markov Processes 1 study Chapter 4 of Haken’s book and complete the tasks of exercise set 3. 04. Markov Processes 2 study the paper Wachtel et al: Fluctuating currents in stochastic thermodynamics. I, Phys. Rev. E 92, 042132 (2015) and complete the tasks of exercise set 4. 05. Brownian Motion, Noise,
consult Chapter 4 of Haken’s book,
study the paper Lebowitz and Spohn, J. Stat. Phys. 96 (1999) 333, and complete the tasks of exercise set 5.
Course. after lectures are resumed Vollmer Wed 11:15 – 12:45 ITP, Brüderstr SR 114 Thu 13:30 – 15:00 ITP, Brüderstr SR 114 Exercise Sessions. Vollmer by appointment
There will be oral exams at the earliest opportunity after the end of the term.
H. Haken Synergetics. An Introduction Springer 1983. an excellent introduction to key ideas from a physics perspective
Feller An Introduction to Probability Theory and its Applications, Vol 1 Wiley 1968. an excellent introduction to key ideas from a mathematics perspective
van Kampen Stochastic Processes in Physics and Chemistry Elsevier 1981 a rich source for applications in physics, in particular of Master equations
specialized sources worth considering: Risken The Fokker-Planck Equation Springer 1989 Gardiner Handbook of Stochastic Methods Springer 1985 Redner A Guide to First-Passage Processes Cambridge 2001
visionary classical texts: Einstein Investigations on the Theory of the Brownian Motion Dover 1956 Hill Free Energy Transduction and Biochemical Cycle Kinetics Dover 2005