Comment on ‘The Aestivation Hypothesis for Resolving Fermi’s Paradox’


In their article, ‘That is not dead which can eternal lie: the aestivation hypothesis for resolving Fermi’s paradox’, Sandberg et al. try to explain the Fermi paradox (we see no aliens) by claiming that Landauer’s principle implies that a civilization can in principle perform far more (\({\sim } 10^{30}\) times more) irreversible logical operations (e.g., error-correcting bit erasures) if it conserves its resources until the distant future when the cosmic background temperature is very low. So perhaps aliens are out there, but quietly waiting. Sandberg et al. implicitly assume, however, that computer-generated entropy can only be disposed of by transferring it to the cosmological background. In fact, while this assumption may apply in the distant future, our universe today contains vast reservoirs and other physical systems in non-maximal entropy states, and computer-generated entropy can be transferred to them at the adiabatic conversion rate of one bit of negentropy to erase one bit of error. This can be done at any time, and is not improved by waiting for a low cosmic background temperature. Thus aliens need not wait to be active. As Sandberg et al. do not provide a concrete model of the effect they assert, we construct one and show where their informal argument goes wrong.

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  1. 1.

    Note that if the photon mass is non-zero, this will become relevant at the extremely cold temperatures, \(k_B\cdot (10^{-31}\,\mathrm {K}) \sim 10^{-35}\,\mathrm {eV/c^2}\), necessary to obtain the computational enhancements Sandberg et al. assert. The experimental upper bound on the photon mass is \(10^{-18}\,\mathrm {eV/c^2}\) [5].

  2. 2.

    It’s possible to construct counterexample for which \(S + N\ln 2 < S_\mathrm {max}\) but there do not exist reversible physical transformations, formalized as Hamiltonian flow in the joint memory-reservoir phase space, that move all entropy from the memory to the reservoir. However, this can only be done by appealing to constraints that do not follow from the first or second laws of thermodynamics. This is not relevant in the present context because we are rebutting the thermodynamic arguments of Sandberg et al., and because matter content of the actual universe clearly has the ability to absorb huge amounts of entropy without ejecting it into the CMB.

  3. 3.

    Note that the proton lifetime is constrained to be greater than \({\sim }10^{29}\) years [5], much larger than the \({\sim }10^{12}\)-year timescale on which the effective temperature of the CMB bath reaches its fixed point on account of CMB photons redshifting below the de-Sitter temperature \(T_f \equiv T_{\mathrm {dS}} \approx 2.7\cdot 10^{-30}\) K [6].


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    Some authors use “reservoir” to refer to effectively infinite system with exogenously controlled parameters, and call everything finite simply a “system”

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    Although we prefer the proper American spelling “estivation”, we adopt Sandberg et al.’s British convention and save our spelling criticism for a different venue

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Research at Perimeter Institute is supported by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Research, Innovation and Science.

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Correspondence to C. Jess Riedel.

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Appendix A: Other Criticism

Here we make additional and less important comments. They are independent and so are not necessary to understand our main criticism above.

Appendix A.1: Thermodynamic Costs of Computation Beyond Erasure

Consider these quotes:

If advanced civilizations do all their computations as reversible computations, then it would seem unnecessary to gather energy resources (material resources may still be needed to process and store the information). However, irreversible operations must occur when new memory is created and in order to do error correction...the actual correction is an irreversible operation...Error rates are suppressed by lower temperature and larger/heavier storage. Errors in bit storage occur due to classical thermal noise and quantum tunneling.

Our most physically realistic models of computation, Brownian computers, have another big entropy cost of computation: “friction” due to driving motion “forward” at a finite rate [3, 7]. This entropy cost per gate operation goes inversely as the time taken per gate operation. If errors happen at a constant physical rate, then trading these costs sets an entropy-cost minimizing time period per gate operation. If stored negentropy were the limiting resource, and not for example computer hardware, then this would set an optimal rate for using negentropy.

Sandberg et al. instead treat error correction as the only entropy cost, and thus say that the min entropy compute strategy is to wait until the universal background temperature reaches a low level.

Appendix A.2: Reversibility of Cooling

This sentence in Ref. [1] is incorrect, possibly for similar reasons as we discuss above:

While it is possible for a civilization to cool down parts of itself to any low temperature, the act of cooling is itself dissipative since it requires doing work against a hot environment.

Cooling does not need to be dissipative. That is, cooling a system requires negentropy but it does not necessarily destroy it; the negentropy used can be recovered if the system is allowed to warm up again. For instance, given a charged battery and two thermal reservoirs at the same temperature, negentropy can be extracted from the battery (in the form of an applied electromotive force, discharging the battery) and transfered to the reservoirs using a reversed Carnot cycle that pumps heat from the one to the other (resulting in a net temperature difference between them). This process is adiabatic and hence reversible.

Thus the fact that error rates can rise with temperature is a reason to run a computer at a low temperature, but not necessarily a reason to wait for low universal background temperatures.


The most efficient cooling merely consists of linking the computation to the coldest heat-bath naturally available.

Allowing heat to directly flow from something warm (the computational machinery) freely to something cool (the bath) unnecessarily increases entropy, and so is not the most efficient method.

Appendix B: Total Work Extractable from a Reservoir-Bath Differential

Here we calculate how much total useful work can be extracted from a reversible engine (e.g., Carnot) operating between an infinite thermal bath at temperature T and a finite thermalized reservoir at initial temperature \(T_0>T\) if the reservoir is assumed to have constant heat capacity C. It is known that the infinitesimal work \({ dW}\) generated by a Carnot engine is related to the heat leaving a reservoir \(\textit{dQ}_R\) and the heat entering the bath \(\textit{dQ}_B\) by the relations

$$\begin{aligned} \textit{dQ}_R&= \textit{dQ}_B + { dW} \qquad&\mathrm {(conservation\, of\, energy)} \end{aligned}$$
$$\begin{aligned} \frac{{ dQ}_R}{{ dQ}_B}&= \frac{T_R}{T} \qquad&\mathrm {(reversible\, heat\, engine)}\, \end{aligned}$$
$$\begin{aligned} C&= \frac{\textit{dQ}_R}{\textit{dT}_R} \qquad&\mathrm {(constant\, heat\, capacity)} \end{aligned}$$

where \(T_R\) is the instantaneous temperature of the reservoir. The total work is obtained by integrating \({ dW}\) from the initial condition \(T_R = T_0\) to the asymptotic final state \(T_R = T\):

$$\begin{aligned} \begin{aligned} W&= \int \textit{dW} = \int (\textit{dQ}_R - \textit{dQ}_B) = \int \textit{dQ}_R (1-T/T_R) \\&= C \int ^{T_0}_T \textit{dT}_R (1-T/T_R) = C T (\beta - 1 - \ln \beta ) \end{aligned} \end{aligned}$$

where \(\beta \equiv T_0/T\). This work can be used to power the bit eraser at the Landauer limit, yielding

$$\begin{aligned} N = \frac{W}{k \, T \ln 2} = \frac{C}{k \ln 2}(\beta - 1 - \ln \beta ) \end{aligned}$$


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Bennett, C.H., Hanson, R. & Riedel, C.J. Comment on ‘The Aestivation Hypothesis for Resolving Fermi’s Paradox’. Found Phys 49, 820–829 (2019).

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  • Foundations of computation
  • Aestivation
  • Thermodynamics of computation
  • Landauer’s principle
  • Fermi’s paradox
  • Adiabatic computing
  • Classical information theory