  Lagrangians can differ by a total derivative without altering the equations
of motion, thus encoding the same physics. This is in general true both
classically and quantum mechanically. We show, however, that in the context of
open quantum systems, two Lagrangians that differ by a total derivative can
lead to different physical predictions. We then discuss the criterion that
allows one to choose between such Lagrangians. Further, starting from the
appropriate QED Lagrangian, we derive the master equation for the
non-relativistic electron interacting with thermal photons upto second order in
the interactions. This case study lends further phenomenological support to our
proposed criterion.
