Quark matter nucleation in hot hadronic matter

We study the quark deconfinement phase transition in hot $\beta$-stable hadronic matter. Assuming a first order phase transition, we calculate the enthalpy per baryon of the hadron-quark phase transition. We calculate and compare the nucleation rate and the nucleation time due to thermal and quantum nucleation mechanisms. We compute the crossover temperature above which thermal nucleation dominates the finite temperature quantum nucleation mechanism. We next discuss the consequences for the physics of proto-neutron stars. We introduce the concept of limiting conversion temperature and critical mass $M_{cr}$ for proto-hadronic stars, and we show that proto-hadronic stars with a mass $M < M_{cr}$ could survive the early stages of their evolution without decaying to a quark star.