  We derive a bound for entropy production in terms of the mean of normalizable
path-antisymmetric observables. The optimal observable for this bound is shown
to be the signum of entropy production, which is often easier determined or
estimated than entropy production itself. It can be preserved under coarse
graining by use of a simple path grouping algorithm. We demonstrate this
relation and its properties using a driven network on a ring, for which the
bound saturates for short times for any driving strength. This work can open a
way to systematic coarse graining of entropy production.
