  We study the scaling properties of the statistics of the work done on a
generic many-body system at a quantum phase transition of any order and type,
arising from quenches of a driving control parameter. For this purpose we
exploit a dynamic finite-size scaling framework. Namely, we put forward the
existence of a nontrivial finite-size scaling limit for the work distribution,
defined as the large-size limit when appropriate scaling variables are kept
fixed. The corresponding scaling behaviors are thoroughly verified by means of
analytical and numerical calculations in two paradigmatic many-body systems as
the quantum Ising model and the Bose-Hubbard model.
