[Self reply because this more or less concerns all replies to parent I have seen so far.] "sorting is not reversible"/"you can't know [the original order]"/"so

[Self reply because this more or less concerns all replies to parent I have seen so far.] "sorting is not reversible"/"you can't know [the original order]"/"sorting loses information" These replies are have two problems in common: 1. They are wrong in the context of reversible gates, because (as I have hinted in my comment) when you sort bits using a normal reversible gate, then the original order of the bits will be encoded in the unused gate outputs. No information is lost, that's why we call these gates reversible in the first place. 2. The heart of my speculation lies in the question if a special irreversible circuit could be integrated into a reversible CPU, which moves bits into order without unnecessarily grounding charges. The more I think about it, the more I tend to think it could. Edit: To make a clearer point on where I'm coming from here: I view reversibility not as a goal in itself, but a tool to use to get ultra low power compute capabilities. To achieve this, the unused output charges need to be recycled into the system. If you solve that problem, you have achieved the goal.