Dyson's eternal intelligence

Dyson's eternal intelligence (the Dyson Scenario), is a hypothetical concept, proposed by Freeman Dyson in 1979, by which an immortal society of intelligent beings in an open universe may escape the prospect of the heat death of the universe by performing an infinite number of computations (as defined below) even though expending only a finite amount of energy.

Freeman Dyson in 2005

Bremermann's limit can be invoked to deduce a lower bound on the amount of time required to distinguish two discrete energy levels of a quantum system using a quantum measurement. [1] One can interpret this measurement as a computation on 1 bit for this system; however, Bremermann’s limit is difficult to interpret physically, since there exist quantum Hamiltonians for which this interpretation would give arbitrarily fast computation speeds at arbitrarily low energy.[2][3] Following this interpretation, the upper bound on the number of such measurements that can be performed grows over time. Assuming that the energy in the quantum system on which the measurement is performed is lost (while ignoring energy that is lost due to the measurement apparatus itself), the energy available from the mechanism suggested below slows logarithmically, but never stops.

The intelligent beings would begin by storing a finite amount of energy. They then use half (or any fraction) of this energy to power their computation. When the energy is used up, they would enter a state of zero-energy-consumption until the universe cooled. Once the universe had cooled sufficiently, half of the remaining half (one quarter of the original energy) of the intelligent beings' fuel reserves would once again be released, powering a brief period of computation once more. This would continue, with smaller and smaller amounts of energy being released. As the universe cooled, the computations would be slower and slower, but there would still be an infinite number of them.[4][5]

In 1998, it was discovered that the expansion of the universe appears to be accelerating rather than decelerating due to a positive cosmological constant, implying that any two regions of the universe will eventually become permanently separated from one another. Dyson noted that "in an accelerated universe everything is different".[6] However, even if the cosmological constant is ${\displaystyle 0}$, the matter density in an FLRW universe would converge to ${\displaystyle 0}$ at rate ${\displaystyle t^{-1/2}}$,[7] suggesting that the stored energy would become unavailable even if it is not used.