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It has been suggested that the overdense region as a result ofinhomogeneities in the early Universe would have undergone a collapse into theprimordial black holes(PBH). In this work, we discuss a possible constraint onthe PBH formation in the radiation dominated epoch by imposing the generalizedsecond law of thermodynamics in the context of spherically collapsing scenario.It is found that both the critical temperature $T_c$ over which the formationof PBH is not possible and the lower bound on the mass of PBH depend on thenumber of degrees of freedom at the time of PBH formation. In the standardmodel, one can show that the lower bound on the mass of PBH known in theliterature, of order Planck mass, is consistent with the thermodynamicconstraint constructed in this work. We also pointed out the possibility thatthe critical temperature(lower bound on PBH mass) can be lowered(increased)provided the number of relativistic degrees of freedom of the Universe isincreasing substantially beyond the standard model.Comment: 6 pages, accepted for publication in PR

Thermodynamic constraint on primordial black hole formation in the radiation dominated epoch