For α α = 0 the fulfillment of the second law depends on the entropy production of the other baths, which should compensate for the negative entropy production of the cold bath. The first formulation of the third law modifies this restriction. Instead of α α ≥ ≥ 0 the third law imposes α α > 0 , guaranteeing that at absolute zero the entropy production at the cold bath is zero: S ˙ ˙ c = 0 . This requirement leads to the scaling condition of the heat current J c ∝ ∝ T c α α + 1 .