Prof. R. Kleeman (Courant Institute NYU)
Many important dynamical systems
can be viewed in space and time at both large and fine scales. Within
physics the analysis of such systems such as gases and liquids has a
long and well developed history which is today rather sophisticated
mathematically. The methods used are referred to generically as
statistical physics. They have, since their development in
mathematical physics, seen widespread and useful application in many
areas outside their origin. This course provides an introductory
overview of the subject aimed at those who would like to adapt such
methods to other fields of interest.
The course will be a seminar course with assessment through attendance only. There will be 11 Lectures covering the following topics:
The course will be a seminar course with assessment through attendance only. There will be 11 Lectures covering the following topics:
- Introduction. Concept of entropy and macro and micro states.
- Basic mathematical concepts from probability and information theory.
- Thermodynamics Part I
- Thermodynamics Part II
- Statistical Equilibrium Ensembles (Microcanonical, Canonical and Grand Canonical). Gibbs theory and equilibrium distributions.
- Application to ideal gases and the connection to thermodynamics.
- Fluctuations.
- Disequilibrium I: Stochastic processes.
- Disequilibrium II. Boltzmann's transport equation and H-Theorem.
- Near-equilibrium theory I: Fluctuation Dissipation Theorem.
- Near-equilibrium theory II: Mori-Zwanzig equation.