  We study the universality of work statistics of a system quenched through a
quantum critical surface. By using the adiabatic perturbation theory, we obtain
the general scaling behavior for all cumulants of work. These results extend
the studies of Kibble-Zurek mechanism scaling of work statistics from an
isolated quantum critical point to a critical surface. As an example, we study
the scaling behavior of work statistics in the two-dimensional (2D) Kitaev
honeycomb model featured with a critical line. By utilizing the trace formula
for quadratic fermionic Hamiltonian, we obtain the exact characteristic
function of work of the 2D Kitaev model at zero temperature. The results
confirm our prediction.
