  In this paper we revisit thermodynamic constraints on primordial black hole
(PBH) formation in the early universe. Under the assumption that PBH mass is
equal to the cosmological horizon mass, one can use the 2nd Law of
Thermodynamics to put a lower limit on the PBH mass. In models of PBH
formation, however, PBHs are created at some fraction of the horizon mass. We
show that this thermodynamic constraint still holds for sub-horizon PBH
formation.
