Using the operational framework of completely positive, trace preserving operations and thermodynamic fluctuation relations, we derive a lower bound for the heat exchange in a Landauer erasure process on a quantum system. Our bound comes from a nonphenomenological derivation of the Landauer principle which holds for generic nonequilibrium dynamics. Furthermore, the bound depends on the nonunitality of dynamics, giving it a physical significance that differs from other derivations. We apply our framework to the model of a spin-$1/2$ system coupled to an interacting spin chain at finite temperature.

• Received 25 February 2014

DOI:https://doi.org/10.1103/PhysRevLett.114.060602