  From the point of view of time-dependent Ginzburg Landau (TDGL) theory, a
Josephson-like relation is derived for an Abrikosov vortex lattice accelerated
and deformed by applied fields. Beginning with a review of the Josephson
Relation derived from the two ingredients of a lattice-kinematics assumption in
TDGL theory and gauge invariance, we extend the construction to accommodate a
time-dependent applied magnetic field, a floating-kernel formulation of normal
current, and finally lattice deformation due to the electric field and inertial
effects of vortex-lattice motion. The resulting Josephson-like relation, which
we call an Extended Josephson Relation, applies to a much wider set of
experimental conditions than the original Josephson Relation, and is explicitly
compatible with the considerations of TDGL theory.
