  We compare the irreversible work produced in an infinitesimal sudden quench
of a quantum system at zero temperature with its ground state fidelity
susceptibility, giving an explicit relation between the two quantities. We find
that the former is proportional to the latter but for an extra term appearing
in the irreversible work which includes also contributions from the excited
states. We calculate explicitly the two quantities in the case of the quantum
Ising chain, showing that at criticality they exhibit different scaling
behavior. The irreversible work, rescaled by square of the quench's amplitude,
exhibits a divergence slower than the fidelity susceptibility one. As a
consequence, the two quantities obey also different finite-size scaling
relations.
