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Comment by ballenf | Hacker News Reader

A couple questions:

1. How does "reversible" here apply to encryption algorithms? In a sense the encryption key is forgotten, but with enough computing power it can be derived from the output (at least for certain encryption methods). So, in a sense no information is lost.

2. If two separate computers perform the same reversible operation, but one in reverse, are the two computers (if considered as one system) consuming no energy? Or must the operations be performed on the same computer sequentially?

If the system of two computers is valid, then does that mean that somehow certain operations / calculations produce energy and others consume it?

I realize both these questions are somewhat nonsensical, so I clearly am missing something fundamental about this theory.

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Reversible (in the paper's sense) is more about the paths information takes than whether it's recoverable in principle. Lossless compression is reversible, but a reversible computer performing it would still need to have storage equal to the size of the entire original data.

It's also important to note that the fact that you are doing calculations isn't the direct cause of energy consumption. Landhauer's principle is a consequence of the second law of thermodynamics, which mandates certain heat losses in certain situations but doesn't tell you anything about how they happen. The question of what actually causes the second law of thermodynamics to hold at the level of fundamental interactions is called Loschmidt's paradox, and there's not really a consensus as to whether we have an answer.

" it would still need to have storage equal to the size of the entire original data."

I think it's worse than this. You need the intermediate steps as well. So, for every and/or type calculation which looks like multiple inputs one output, you need to keep all the input bits.

Feynman has an interesting chapter on this in his lectures on computation, including a cool billiard ball computer (a la Ed Fredkin I think).

On 2. You can't run reversible logic on our currently non-reversible logic and expect to see less power usage. If you had two reversible computers you could reverse the output of the other while consuming minimal energy just as a single reversible computer could reverse it's own output. The operations must be run forward at least once, or technically you don't have the outputs to input to the reverse.

For 1., I don't think reversible computing relates to finding inverse functions of algorithms but rather considering how it might be possible reversing the operations while retaining whatever memory is required to reverse irreversible operations

2. Reversible operations have no minimum amount of energy that must be dissipated as heat, unlike irreversible operations which must dissipate every time bits are erased. So each computer individually could be consuming no energy, so both together would consume the sum (zero) of the two.

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