On Tue, Mar 13, 2012  Bruno Marchal <marc...@ulb.ac.be> wrote:

> It looks like computation would need energy, but the energy is needed
> only for erasing information, and since a paper by Hao Wang (universal, and
> thus all) computations can be done without ever erasing information.

Yes, with a reversible computer information is not erased, you'd still need
energy but the amount needed to make a calculation can be made arbitrarily
small, however the only way to do that is by slowing down the calculation.
Fortunately even a small reduction in speed can help a lot in energy
saving, the power dissipation (per unit of time) falls as the square of the
speed. We won’t know if that’s good enough to allow infinite computation
until we know more about the basic laws of physics and cosmology, and it
may not be possible to learn that from mathematics alone.

Today's computers are not reversible because there is no reason for them to
be, in our big clunking machines the theoretical limits from the
thermodynamics of computation is just not important compared with other
factors. But a nanocomputer would almost have to be reversible, otherwise it
would generate so much heat it would be more like a bomb than a computer.

  John K Clark

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