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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.

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While not a book (though it comes with a guide), The Science of Information From Language to Black Holes by Benjamin Schumacher starts off with the premise that information is physical. This course requires only basic math (for example, the information inequality is demonstrated with an example rather than proved using Jensen's inequality). However, the ideas were clearly conveyed and each lecture was well structured, with easy to follow and illustrative examples. The "It from Bit: Physics from Information" lecture specifically covers black holes and the holographic principle (at a high level, of course).

Schumacher references two other sources, Decoding the Universe by Seife and The Bit and the Pendulum: From Quantum Computing to M Theory--The New Physics of Information by Siegfried (which itself quotes references Schumacher). I only read a good part of the first of these and skimmed the second, but both of these are popular-level books. The parts of Decoding the Universe I read were pretty smooth to get through. The author did a good job of conveying essential concepts to a general audience.

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