This was my first gut instinct, except even simpler than Maxwell's demon: by partitioning the apparatus with the mirror, you're altering the statistical ensembl

This was my first gut instinct, except even simpler than Maxwell's demon: by partitioning the apparatus with the mirror, you're altering the statistical ensemble of possible wave states (increasing the relative information entropy) and that's where your energy comes from. That's just my gut though, I'm not a professional physicist.