Nonequilibrium Extension of the Landau-Lifshitz-Gilbert Equation for   Magnetic Systems
  Using the invariant operator method for an effective Hamiltonian including the radiation-spin interaction, we describe the quantum theory for magnetization dynamics when the spin system evolves nonadiabatically and out of equilibrium, $d \hat{\rho}/dt \neq 0$. It is shown that the vector parameter of the invariant operator and the magnetization defined with respect to the density operator, both satisfying the quantum Liouville equation, still obey the Landau-Lifshitz-Gilbert equation. 
Jeongwon Ho, B. C. Choi (U. Victoria), F. C. Khanna, Sang Pyo Kim   (Kunsan Nat'l Univ.)