[DonHopkins]

There's some interesting explanation about the thermodynamics of reversible cellular automata in these papers:

INVERTIBLE CELLULAR AUTOMATA: A REVIEW. Tommaso Toffoli and Norman Margolus. MIT Laboratory for Computer Science.

Because of this "information-losslessness" (ach!), ICA automatically obey the second principle of thermodynamics and, more generally, display a full-featured statistical mechanics analogous to that of Hamiltonian systems. As additional structure is introduced (for instance, particle conservation), macroscopic mechanical features such as elasticity, inertia, etc. naturally emerge out of statistics itself. In sum, once we make sure that it is conserved, information has an irresistible tendency to take on a strikingly tangible aspect (cf. [73]) to materialize itself.

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.27....

When -- and how -- can a cellular automaton be rewritten as a lattice gas? Tommaso Toffolia, Silvio Capobiancob, Patrizia Mentrastic.

https://www.sciencedirect.com/science/article/pii/S030439750...

Reversible computing and cellular automata - A survey. Kenichi Morita.

https://www.sciencedirect.com/science/article/pii/S030439750...

On Invertible Cellular Automata. Karel Culik II.

http://www.complex-systems.com/pdf/01-6-1.pdf

One of the tripper far-reaching (to the end of the universe) applications of reversible computation is Tipler's "Omega Point," which he wrote about in "The Physics of Immortality".

https://www.wired.com/2002/12/holytech/

https://en.wikipedia.org/wiki/Omega_Point

https://en.wikipedia.org/wiki/Frank_J._Tipler#The_Omega_Poin...

[perl4ever]

Tipler's Omega Point prediction doesn't seem like it would be compatible with the expanding universe, would it? Eventually everything will disappear over the speed-of-light horizon, and then it can't be integrated into one mind.

[DonHopkins]

It also wishfully assumes that the one mind can't think of better things to do with its infinite amount of cloud computing power than to simulate one particular stone age mythology.

Then again, maybe it's something like the 1996 LucasArts game Afterlife, where you simulate every different religion's version of heaven and hell at once.

https://en.wikipedia.org/wiki/Afterlife_(video_game)

The primary goal of the game is to provide divine and infernal services for the inhabitants of the afterlife. This afterlife caters to one particular planet, known simply as the Planet. The creatures living on the Planet are called EMBOs, or Ethically Mature Biological Organisms. When an EMBO dies, its soul travels to the afterlife where it attempts to find an appropriate "fate structure". Fate structures are places where souls are rewarded or punished, as appropriate, for the virtues or sins that they practiced while they were alive.