  We study properties of the work distribution of a many-body system driven
through a quantum phase transition in finite time. We focus on the
non-Gaussianity of the distribution, which we characterize through two
quantitative metrics: skewness and negentropy. In particular, we focus on the
quantum Ising model and show that a finite duration of the ramp enhances the
non-Gaussianity of the distribution for a finite size system. By examining the
characteristics of the full distribution, we observe that there is a clear
intermediate regime between the sudden quench and adiabatic limits, where the
distribution becomes increasingly skewed.
