Tool 18 · Aestivation cost calculator
The thermodynamic case for hibernation — and the counter-argument
Landauer’s principle says every irreversible bit operation costs at least kB T ln 2 joules in heat dissipation. Lower the temperature, lower the cost. Sandberg et al. (2017) showed that waiting 1012–1013 yr for the CMB to cool from 2.73 K to < 10−3 K multiplies the irreversible-ops budget per joule by a factor of order 1030. The gain is genuine and enormous — if the limiting factor is Landauer cost and if the cold future reservoir is genuinely new (not accessible today). Bennett, Hanson & Riedel (2019) contested exactly this conditional: deep space is already at ~3 K or colder today; a sufficiently large radiator can already approximate the future cold sink. If you can dissipate into a ∼3 K reservoir right now, you capture most of the gain without waiting. The reversibility fraction slider in the tool separates the two cases: near-zero reversibility means you pay full Landauer cost and aestivation gives a 1030× gain; near-one reversibility means you pay almost nothing now and the waiting gain vanishes.
Step payoff
Read the "gain vs. wait" panel: at Δt = 10¹² yr and fully irreversible computing (rev = 0), Sandberg's ×10³⁰ gain appears. Switch to near-reversible (rev = 0.999) and the gain collapses to near-zero — the Bennett counter-argument. The tool shows both numbers side by side so you can see which scenario you're in. The question for the MTH is: does it matter? The ergosphere provides a gain that is neither thermal nor reversibility-dependent.
⚠ Bennett, Hanson & Riedel 2019 counter-argument
Cold space (~3 K background, < 10 K in deep inter-cluster voids) is already available as a heat sink. The aestivation gain is only real if the future low-temperature reservoir is genuinely unavailable now. If you can build a large enough radiator today — which is not obviously impossible for a K-II or K-III civilisation — you capture the Landauer gain without waiting 10¹² years. Sandberg's response: the total future temperature is lower, not just accessible, and the gain is also larger in absolute magnitude. The debate is unresolved in the literature.