His Phase Space chart is just a visualization of the 2nd law of thermodynamics. Its just showing that the universe goes from low entropy to high entropy and eventually end in thermal equilibrium.
His theory does not really center around the phase space chart . The diagram makes no new claims its just a visualization of 2nd law thermodynamics.
His theory centers around how the end of the universe in its infinity is the same as (or leads to) the infinity of the beginning. From what I can understand certain conditions remain at the end at are in common with the beginning. 1) only energy is left. 2) density variations are present as gravitational waves. 3) time-space is lost or redefined. Maybe its the same in the math.
I am still a little fussy as to why time-space is lost. Time is lost some how because with no mass there is nothing to keep track of time or nothing that is influenced by it. So if one second passes or an eternity passes it would not make a difference to the energy that is left in the universe. As for space, I'm not too sure. But somehow the infinite space would be the zero space that is the singularity of the big bang.