  We study the physics of quantum phase transitions from the perspective of
non-equilibrium thermodynamics. For first order quantum phase transitions, we
find that the average work done per quench in crossing the critical point is
discontinuous. This leads us to introduce the quantum latent work in analogy
with the classical latent heat of first order classical phase transitions. For
second order quantum phase transitions the irreversible work is closely related
to the fidelity susceptibility for weak sudden quenches of the system
Hamiltonian. We demonstrate our ideas with numerical simulations of first,
second, and infinite order phase transitions in various spin chain models.

Quantum Physics;Statistical Mechanics