You are the leader of a far-future civilization - human or otherwise - that has endured for trillions of years doing whatever far-future civilizations do. You've surrounded stars with Matrioshka brains and gathered them up with stellar engines, pooled as much mass as you could and did all the computation theoretically possible, but energy is the real problem.
You know you're going to run out of extractable heat soon enough. Black holes radiate too slowly, and while they get stronger in their last moments, they ultimately vanish.
Luckily, your universe contains an anomaly, something totally unique, contrary to the laws of thermodynamics, and, as far as you're aware, totally indestructible and immutable. The anomaly is a single object of a certain size that constantly radiates at a specific temperature, thus producing a constant amount of power.
You wish to maintain your civilization, even if you have to upload your people to computers and shrink them down to a microscopic scale to run everything off the anomaly, for the rest of the infinite span of time past the heat death.
The minimum requirement is the continual, uninterrupted simulation of the equivalent of at least one million human brains for a time that exceeds any finite value given.
How small and cool can the anomaly be?
You have access to:
- The combined knowledge of a far-future civilization gathered over its lifespan. No technological holds are barred provided they make some physical sense. Super-intelligence is fair game. Assume mind uploading is practical.
- Several trillion solar masses of initial material of your choice.
- A few billion active stars and all the initial energy they can provide.
- One anomaly that is your only thermodynamics-violating object.
You may have to worry about:
- Proton decay and quantum tunnelling. How do you replace parts of your computing system as they go missing or fuse into each other? Do you synthesize new matter out of energy - and can you do that if your energy source is only at infrared or even radio wavelengths? (Or does it have to be brighter or hotter?)
- Logistics. Computing systems must be able to simulate everyone and keep track of the physical world with sensors, repairing damage and the like.
- Sanity. Can a simulation that lasts forever even provide infinite utility to its occupants? Will you resort to memory-wiping or are there other options that a sufficient amount of energy can help provide? (How much will you need?)