I image a cyclic evolution that ends with a solitary or ”singular” point/vacuum. That would be a distinct case of gravity potential. Assuming a quantum action of the quantum actor, circulation would accumulate its surface tension or ”charge”. It would divide as from energy density. Time-like aspect would be linear as axis is ”compressed”. Process is unitary and terminated by division at t0. I suspect this relates to math theorems of eternal recurrence that holds for dimensions 1, 2 but not 3. Polya’s Random Walk if I recall correctly. But it requires the vacuum to self-charge and that is disallowed in theory because it makes quantum theory ”trivial”. As for me ”trivial” implies ”probably valid”

If there is a time's arrow (infinite aperiodic evolution), the descriptive complexity of the Universe will increase as a logarithmic function (in base 2) of time (here is the proof of my theorem). Does something that is increasing its descriptive complexity all the time deserve to be called dead? I do not think so.

Another possibility is that time is cyclic. In this case, the evolution of the Universe will be like the finite cellular automata studied by S. Wolfram, e.g., rule 30 and rule 90. After the heat death, there will be a big bang again.

Finally, there is the possibility that the Universe will halt and everything will be frozen forever.