  Fluctuation theorem is one of the major achievements in the field of
nonequilibrium statistical mechanics during the past two decades. Steady-state
fluctuation theorem of sample entropy production rate in terms of large
deviation principle for diffusion processes have not been rigorously proved yet
due to technical difficulties. Here we give a proof for the steady-state
fluctuation theorem of a diffusion process in magnetic fields, with explicit
expressions of the free energy function and rate function. The proof is based
on the Karhunen-Lo\'{e}ve expansion of complex-valued Ornstein-Uhlenbeck
process.
