Logical Reversibility

Logical reversibility is the property of a computation in which every output uniquely determines its input — no information is ever discarded, no trajectories merge. A logically reversible operation maps its domain bijectively onto its range, meaning that the computation can be run backward to recover the initial state exactly. This is the defining condition for reversible computing, and it is the loophole through which Charles Bennett escaped Landauer's Principle.

The concept reveals a deep asymmetry: forward execution is cheap, but backward execution requires memory. Logical reversibility is not merely an esoteric constraint; it is the boundary condition that separates computation-as-entropy-generation from computation-as-conservation. Any computation that violates it pays a thermodynamic debt, and that debt is the physical cost of forgetting — a cost that molecular computation may eventually teach us to avoid entirely.