Large deviation function for entropy production in driven one-dimensional systems

The large deviation function for entropy production is calculated for a particle driven along a periodic potential by solving a time-independent eigenvalue problem. In an intermediate force regime, the large deviation function shows pronounced deviations from a Gaussian behavior with a characteristic ``kink'' at zero entropy production. Such a feature can also be extracted from the analytical solution of the asymmetric random walk to which the driven particle can be mapped in a certain parameter range.