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 for $ heta in left(-frac{pi}2, 0 ight) cup left(0,frac{pi}2 ight)$. The proof is based on the Karhunen-Lo`{e}ve expansion of complex-valued Ornstein-Uhlenbeck process.
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Edited by: Liu Huan & Lang Cuicui |