  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 non-phenomenological derivation of the Landauer principle which
holds for generic non-equilibrium dynamics. Furthermore the bound depends on
the non-unitality 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.
