What I meant was that reversible computation doesn't come for free.

You have to be able to reverse the whole of the computation. If you have inputs coming from the outside you have to have thermodynamically random bits for each input bit (you can then reverse the computation by exposing them to random fluctuations).

If you don't have the pool of randomised bits you have overwrite known bits, which is irreversible.

Depending upon how many randomised bits you start out with, you will run out of them sooner or later and then you will have to increase your memory in real time (spending less energy to do so that using irreversible computation).