>Does this imply that physical entropy and informational entropy are the same?

It does, and there is a very strong (but not universally accepted) case that they are the same thing: https://en.wikipedia.org/wiki/Entropy_in_thermodynamics_and_...

Great lay article about it: http://lesswrong.com/lw/o5/the_second_law_of_thermodynamics_...

(Side note: I've long thought you can derive Carnot efficiency based on information-theoretic arguments about the information contained in knowing only the temperature difference between a heat source and a sink.)

>Does it imply the computer would not give off heat? Or that a significant amount of the heat generated by a computer is due to information loss?

Basically, yes. You can't avoid the heat emission from setting a 0 to a 1 on that computer's storage medium, but you would avoid the loss from any of the intermediate computations that typically make CPUs so hot.

I'm not the person who was asking, but thanks for the insightful comments. Makes sense.

Wouldn't a reversible computer that executes need to take up an exponentially large amount of physical space as it executes?

That might work for small problems but it doesn't seem like it would scale. Or rather, it would scale to fill the known universe.

Sorry I haven't really dug into the attached articles yet, but I will.

See the thread about the asymptotic penalties: https://news.ycombinator.com/item?id=14151390

> Does it imply the computer would not give off heat?

The implication goes the other way: if the computer does not give off heat, it must be reversible.

So, in a sense, heat is unrecoverable information.

In some sense that seems to be true.

But I just meant that while it's easy to make a reversible circuit, no tech we have today can make it as energy efficient as might be theoretically possible.