[datenwolf]

Actually hashes do create entropy (every computation creates entropy in some form or another). What's the entropy of a 4 bit number? What's the entropy of a 4 bit number hashed by a 64 bit hash function? The act of computation does in fact create entropy, as per the 2nd law of thermodynamics, a part of which shows up in the hash.

[pxx]

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

[amelius]

> every computation creates entropy in some form or another

Ok, what is the entropy created by this function that maps a 4-bit number to a 64 bit number:

    0 -> 0
    1 -> 1
    2 -> 1
    3 -> 1
    4 -> 1
    ...
    15 -> 1

[datenwolf]

60 bits. Yes, I know, you can compress it down very well. But consider that entropy in computation involves not just the bits you store, but also the bits that the processor touches and eventually dissipates as heat into the universe.