Dyson has a scenario for infinitely much computation with finitely much energy with cosmological constant zero. Probably you can’t really do infinitely much computation, but end up in a loop because of limited memory.
Dyson suggests that spatially encoding memory in an expanding computer would allow memory capacity to grow logarithmically.
If inflation changes the cosmological constant, then getting it arbitrarily close to zero would be as good as Dyson’s scenario for the purpose of this discussion. You also want regions with arbitrarily high memory, which is probably mainly a matter of energy. My vague impression is that the cosmological constant gives a bound on the computation independent of the amount of memory.
What I recall hearing is that a nonzero cosmological constant makes things fall off the edge of the universe, i.e. the edge is an event horizon, so it Hawking-radiates, so the temperature of the sky (=> energy dissipation per operation) asymptotically approaches something nonzero. There might be a more pure argument.
Dyson suggests that spatially encoding memory in an expanding computer would allow memory capacity to grow logarithmically.
What I recall hearing is that a nonzero cosmological constant makes things fall off the edge of the universe, i.e. the edge is an event horizon, so it Hawking-radiates, so the temperature of the sky (=> energy dissipation per operation) asymptotically approaches something nonzero. There might be a more pure argument.
Yeah, I guess I should have looked that up. I do not find Dyson’s paragraph on memory convincing. Frankly, I take it as evidence of the opposite.