  We propose an alternative method to compute the entropy production of a
classical underdamped nonequilibrium system in a continuous phase space. This
approach has the advantage that it is not necessary to distinguish between even
and odd-parity variables. We show that the method leads to the same local
entropy production as in previous studies while the differential entropy
production along a stochastic trajectory turns out to be different. This
demonstrates that the differential entropy production in continuous phase space
systems is not uniquely defined.
