  The asymptotic energy dissipation is connected to the third-order scaling of
the longitudinal velocity increment magnitude in three-dimensional turbulence
via the Kolmogorov $4/5$ law. It is shown that the third-order longitudinal
absolute velocity increment scaling should not exceed unity for anomalous
dissipation to occur, that is for non-vanishing average dissipation in the
inviscid limit -- also known as the ``zeroth law" of turbulence. Conversely, if
the third-order longitudinal absolute velocity increment scaling exceeds unity
then the average dissipation must asymptotically vanish and the velocity
increment field will becomes symmetric at least at the level of its skewness.
This work highlights the importance of the third-order absolute velocity
increment scaling in assessing the status of the ``zeroth-law" of turbulence.
