  We study a Brownian particle on a moving periodic potential. We focus on the
statistical properties of the work done by the potential and the heat
dissipated by the particle. When the period and the depth of the potential are
both large, by using a boundary layer analysis, we calculate a cumulant
generating function and a biased distribution function. The result allows us to
understand a Zon-Cohen singularity for an extended fluctuation theorem from a
view point of rare trajectories characterized by a negative inverse temperature
of the biased distribution function.
