Also see Dyson’s Eternal Intelligence:

en.wikipedia.org/…/Dyson's_eternal_intelligence

Basically, if you assume it’s possible to upload our intelligence to a computer and run it, then you can keep the energy going to run it for a very, very long time. Well past the heat death of the rest of the universe. It depends on running things in an on and off state to conserve energy for trillions of years. Subjectively, the people in there wouldn’t notice that and would simply see their active lifespans go for trillions of years. It’s not clear what the limit would actually be.

It’s something like Zeno’s Paradox. You cut things in half each cycle, but never quite get to zero.

with only a finite initial store of energy, only a finite number of thoughts can ever be processed. This “thermal death” of the universe prevents the infinite hibernation and computation trick from working, thus rendering Dyson’s eternal intelligence scenario impossible in a universe with a positive cosmological constant.

My disappointment is immeasurable, and my day is ruined.