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The Large Deviation Principle and Steady-state Fluctuation Theorem for the Entropy Production Rate of a Stochastic Process in Magnetic Fields

  • Speaker: Lihu Xu

  • Time: Feb 23, 2017, 16:10-17:10

  • Location: Conference Room 706, Service Center of Scientific Research and Teaching

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 $\theta \in \left(-\frac{\pi}2, 0\right) \cup \left(0,\frac{\pi}2\right)$. The proof is based on the Karhunen-Lo\`{e}ve expansion of complex-valued Ornstein-Uhlenbeck process, in which the key step is solving a Sturm-Liouville problem to determine the free energy function.