  We consider fluctuations of steady-state current activity, and of its dynamic
counterpart, the local current, for the one-dimensional totally asymmetric
simple exclusion process. The cumulants of the integrated activity behave
similarly to those of the local current, except that they do not capture the
anomalous scaling behavior in the maximal-current phase and at its boundaries.
This indicates that the systemwide sampling at equal times, characteristic of
the instantaneous activity, overshadows the subtler effects which come about
from non-equal time correlations, and are responsible for anomalous scaling. We
show that apparently conflicting results concerning asymmetry (skewness) of the
corresponding distributions can in fact be reconciled, and that (apart from a
few well-understood exceptional cases) for both activity and local current one
has positive skew deep within the low-current phase, and negative skew
everywhere else.
