When Black Holes Relax in a Cold Bath: Evolving Page Curves for Black Holes Coupled to Cooling Baths

We consider scenarios where Jackiw-Teitelboim black holes are attached to baths whose temperatures can be manipulated externally. We consider the bath to be cooled continuously and numerically investigate the subsequent evolution of the generalized entropies of the black hole. Page curves corresponding to several different cooling profiles of the bath are obtained.