Large deviation function and fluctuation theorem for classical particle transport

We analytically evaluate the large deviation function in a simple model of classical particle transfer between two reservoirs. We illustrate how the asymptotic long-time regime is reached starting from a special propagating initial condition. We show that the steady-state fluctuation theorem holds provided that the distribution of the particle number decays faster than an exponential, implying analyticity of the generating function and a discrete spectrum for its evolution operator.