I don't think you understand what this conversation is about. We are considering information theoretic entropy, not thermodynamic entropy from the mechanism of

I don't think you understand what this conversation is about. We are considering information theoretic entropy, not thermodynamic entropy from the mechanism of computation itself. The result of applying a deterministic function on a random variable cannot have more entropy than the underlying random variable. This is a theorem, one that is trivial enough to not have a name. But you can find solution sets to homework that will prove it for you: https://my.ece.utah.edu/~rchen/courses/homework1_sol_rr.pdf https://my.ece.utah.edu/~rchen/courses/homework1_sol_rr.pdf