__Information Theory, Predictability and Disequilibrium__

(MATH-GA 2830.00__2__)

** Instructor:** Prof. Richard Kleeman (Office: 929 Warren Weaver)

There will be 11 lectures. The contents are described briefly below. Relatively complete lecture notes as pdf files are linked to below.

__Lecture 1__

Introduction. Overview of Applications. Basic axiomatic derivation following Shannon. Introduction to the information content of codes. Lecture Notes.

__Lecture 2__

Entropic functionals and their properties. Lecture Notes.

__Lecture 3__

Stochastic Processes. Lecture Notes.

__Lecture 4__

Data Compression. Lecture Notes.

__Lecture 5__

Differential Entropy. The limiting process and coarse graining. Invariance properties. Lecture Notes.

__Lecture 6__

Maximum entropy and statistical mechanics. Lecture Notes.

__Lecture 7__

Gaussian special case. Lecture Notes.

__Lecture 8__

Dynamical system statistical prediction. Introduction and commonly used practical methodologies. Lecture Notes.

__Lecture 9__

Theoretical predictability concepts. Lyapunov exponents and their relation to information theory and predictability. An information theory framework for studying predictability. Lecture Notes.

__Lecture 10__

Application of information theoretical techniques to a variety of simple but physically relevant dynamical systems. Lecture Notes.

__Lecture 11__

A new information theoretical approach to disequilibriated statistical systems. This describes recent research by the instructor in statistical physics and predictability theory.