  In the conventional two-point measurement scheme of quantum thermodynamics,
quantum coherence is destroyed by the first measurement. But as we know the
coherence really plays an important role in the quantum thermodynamics process,
and how to describe the work statistics for a quantum coherent process is still
an open question. In this paper, we use the full counting statistics method to
investigate the effects of quantum coherence on work statistics. First, we give
a general discussion and show that for a quantum coherent process, work
statistics is very different from that of the two-point measurement scheme,
specifically the average work is increased or decreased and the work
fluctuation can be decreased by quantum coherence, which strongly depends on
the relative phase, the energy level structure and the external protocol. Then,
we concretely consider a quenched 1-D transverse Ising model, and show that
quantum coherence has a more significant influence on work statistics in the
ferromagnetism regime compared with that in the paramagnetism regime, so that
due to the presence of quantum coherence the work statistics can exhibit the
critical phenonmenon even at high temperature.
