  Driven condensed matter systems consistently pose substantial challenges to
theoretical understanding. Progress in the study of such systems has been
achieved using the Floquet formalism, but certain aspects of this approach are
not well understood. In this paper, we consider the exceptionally simple case
of the rotating Kekul\'e mass in graphene through the lens of Floquet theory.
We show that the fact that this problem is gauge-equivalent to a
time-independent problem implies that the "quasi-energies" of Floquet theory
correspond to a continuous symmetry of the full time-dependent Lagrangian. We
use the conserved Noether charge associated with this symmetry to recover
notions of equilibrium statistical mechanics.
