  When the coupled electron-nuclear dynamics are subjected to strong Floquet
driving, there is a strong breakdown of the Born-Oppenheimer approximation. In
this article, we derive a Fokker-Planck equation to describe non-adiabatic
molecular dynamics with electronic friction for Floquet driven systems. We
first provide a new derivation of the Floquet quantum-classical Liouville
equation (QCLE) for driven electron-nuclear dynamics. We then transform the
Floquet QCLE into a Fokker-Planck equation with explicit forms of frictional
force and random force. We recast the electronic friction in terms of Floquet
Green's functions such that we can evaluate the electronic friction explicitly.
We show that the Floquet electronic friction tensor exhibits antisymmetric
terms even at equilibrium for real-valued Hamiltonian, suggesting that there is
a Lorentz-like force in Floquet driven non-Born Oppenheimer dynamics even
without any spin-orbit couplings.
