  We study the fluctuations of a stochastic Maxwell-Lorentz particle model
driven by an external field to determine the extent to which fluctuation
relations are related to large deviations. Focusing on the total entropy
production of this model in its steady state, we show that, although the
probability density of this quantity globally satisfies (by definition) a
fluctuation relation, its negative tail decays exponentially with time, whereas
its positive tail decays slower than exponentially with time because of long
collision-free trajectories. This provides an example of physical system for
which the fluctuation relation does not derive, as commonly thought, from a
probability density decaying everywhere exponentially with time or, in other
words, from a probability density having a uniform large deviation form.
