@Hafizaad's friend: I'm glad that you made this response.
1) Explosion point is trivial
2)I'm sorry I posted a link that you cannot access, my internet is directly link to university server so I can access all the academic publications for free. as such I didn't know the journal was inaccessible to others. In any case here is a
free version of the same paper.
Heat death happen when this equation holds
S(t+1)=S(t)+dS right? if we can make dS vanishingly small then we can have an infinite process.
What Baum et al are suggesting here is that when the universe is contracting there will be a separate pocket universes devoid of matter, with the exception of dark energy, so these universe can adiabatically, in the normal thermodynamic sense, contract with entropy increasing only infinitesimally.