I am about to finish my undergraduate studies and am very interested in going into the applications of information theory to either general relativity, or quantum mechanics.
However I have been struggling to find any good books or resources in general that discuss how information theory can be used in theoretical physics. To be clear, I am not interested in quantum computers, which most books seem to focus on.
In your recommendations I would appreciate if you could specify the mathematical prerequisites to the book, roughly what topics it covers, and how focused it is on theoretical physics (as opposed to quantum computing).
P.S. I've been told by my professors about how information theory is proving useful in:
Understanding black holes
The holographic principle
Quantum field theory
Understanding the uncertainty principle as a two step algorithm
How gravity can be seen as a consequence of thermodynamics
If anyone knows information theoretic books that cover any of these topics, bonus points.