I am interested in learning about the fundamental limits of computation and in particular would like to read textbooks on the subject if they exist. My background is in maths and computer science - I am certainly not looking for books on complexity theory.
Example questions I am looking to answer/be able to interpret:
- What is the amount of energy required (as a fundamental limit) to divide two numbers?
- What is the smallest volume of space which can retrievably store $n$ bits of data?
- What is the fundamentally shortest running time of an algorithm with $n$ steps? (where steps are suitably defined by some fundamental physical definition of a computer)
I have heard of quantum-information theory, but I'm not sure that's precisely what I'm looking for.