  We prove that the observable telegraph signal accompanying the bistability in
the photon-blockade-breakdown regime of the driven and lossy Jaynes--Cummings
model is the finite-size precursor of what in the thermodynamic limit is a
genuine first-order phase transition. We construct a finite-size scaling of the
system parameters to a well-defined thermodynamic limit, in which the system
remains the same microscopic system, but the telegraph signal becomes
macroscopic both in its timescale and intensity. The existence of such a
finite-size scaling completes and justifies the classification of the
photon-blockade-breakdown effect as a first-order dissipative quantum phase
transition.
