Life, information theory, probability, and physics

Topics in Statistical Physics and Probability Theory

We discuss some basic facts regarding Gibbs measures on the infinite lattice Zd. Our discussion is restricted to an explicit case with nearest-neighbor interactions but the reader should note that the general theory allows much more flexibility; see Friedli and Velenik [3, Chapter 6] for additional details. Preliminaries. Let (S,S, λ) be a measure space (λ is a positive measure, either finite o...

Statistical Physics and Information Theory

This is a set of lecture notes for a graduate course, which focuses on the relations between Information Theory and Statistical Physics. The course is aimed at EE graduate students in the area of Communications and Information Theory, as well as to graduate students in Physics who have basic background in Information Theory. Strong emphasis is given to the analogy and parallelism between Inform...

Information Theory and Statistical Physics

Relationships between information theory and statistical physics have been recognized over the last few decades. One such aspect is identifying structures of optimization problems pertaining to certain information-theoretic settings and drawing analogy to parallel structures arising in statistical physics, and then borrowing statistical mechanical insights, as well as powerful analysis techniqu...

00 1 Physics with exotic probability theory

Probability theory can be modified in essentially one way while maintaining consistency with the basic Bayesian framework. This modification results in copies of standard probability theory for real, complex or quaternion probabilities. These copies, in turn, allow one to derive quantum theory while restoring standard probability theory in the classical limit. The argument leading to these thre...

Some Concepts in Probability and Information Theory