In structures made up of alternating superconducting and ferromagnet layers (S/F/S heterostructures), it is known that the macroscopic quantum wave function of the ground state changes its phase difference across the F layer from 0 to pi under certain temperature and geometrical conditions, hence the name “0–pi” for this crossover. We present here a joint experimental and theoretical demonstration that 0–pi is a true thermodynamic phase transition. Microwave measurements of the temperature dependence of the London penetration depth in Nb/Pd0.84Ni0.16/Nb trilayers reveal a sudden, unusual decrease of the density of the superconducting condensate (square modulus of the macroscopic quantum wave function) with decreasing temperature, which is predicted by the theory here developed as a transition from the 0 state to the pi state. Our result for the jump of the amplitude of the order parameter is a thermodynamic manifestation of such a temperature-driven quantum transition.