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I plan six lectures on possible directions of modification/generalization of the probability theory, both concerning mathematical foundations and applications within and without pure mathematics. Specifically, I will address two issues.
1. Enhancement of stochastic symmetry by linearization and Hilbertization of set-theoretic categories.
2. Non-symmetric probability theory in heterogeneous environments of molecular biology and of linguistics.
I will start with a category theoretic view on probability and entropy. This includes
Next I will present several linearized measure-like structures, and associated entropies, such as the homology measures and their appearance in many particle systems.
Also I say something about the von Neumann entropy.
Finally I will dicuss possible concepts of probability for heterogeneous systems, such as natural languages and their applications to automatic signals/texts analysis in the spirit of my article Ergostructures, Ergodic and the Universal Learning Problem: Chapters 1, 2.
(The above mentioned papers can be found on my web page at IHES in the section "recent").