  In this work, we study the stochastic dynamics of micro-magnetics interacting
with a spin-current torque. We extend the previously constructed stochastic
Landau-Lifshitz equation to the case with spin-current torque, and verify the
conditions of detailed balance. Then we construct various thermodynamics
quantities such as work and heat, and prove the second law of thermodynamics.
Due to the existence of spin-torque and the asymmetry of the kinetic matrix, a
novel effect of entropy pumping shows up. As a consequence, the system may
behave as a heat engine which constantly transforms heat into magnetic work.
Finally, we derive a fluctuation theorem for the joint probability density
function of the pumped entropy and the total work, and verify it using
numerical simulations.
