  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.
