Yeah. Stapledon is older - Star Maker was written in 1937, and it builds on the themes of Last and First Men, a book he wrote in 1930. They don't really have much plot to speak of, they're more purely exploratory and written as a kind of future history/scifi cosmogony/speculative evolutionary engineering/secular eschatology. But they're quick reads and I think they're interesting worldbuilding thought experiments.

I do think there's some inspiration of that type that goes on, yes. But also, it is often possible for a field to know early on what some of the theoretical limits are for what can be achieved through it, even if it takes decades or more to even start seeing it happen. The great scifi authors are the ones that ask what it will mean when they do.

Hey, sorry, I thought I'd responded to this one and apparently hadn't.

I think my black hole discussion is essentially my answer to (1). I don't think I could think of a way to make it work with an asteroid or similar setup. I am not entirely sure your discussion of cosmological degradation is well-defined enough to  answer more precisely than that.

For (2), my other comments about you can of course do work to create a gradient you then consume, and get some of the work back. But as written, no, that doesn't mean the setup as described can work.

I can't take much credit, they're ideas generally in the zeitgeist at the boundary of physics, sci-fi, and speculative engineering.

If you like sci-fi, and haven't read these already, you may want to check out Asimov's short story The Last Question, William Olaf Stapledon's short novel Star Maker, and Clarke's trilogy A Time Odyssey. All have elements of "What would it take and look like for a civilization to actually survive into the utmost future, long after all the stars have burned out?" They don't talk about these specific mechanisms (the first two were from before we knew about the CMB!) but I find them really interesting and thought provoking.

I would say that if you find a place in the universe where there exists any kind of free energy gradient - any differential in pressure, temperature, composition, or other 'structure' as you've been calling it - then with Sufficiently Advanced (TM) technology you can extract work from it. If you're Sufficiently Smart and patient you may be able to build the equipment in a way that allows you to later reversibly extract the work that went into its construction.

What you can't do is start from a lack of such gradients, and create a system that causes them to passively form. As described, your system can't work, because it's trying to claim it can have passive diffusion that is net in one direction, and work extraction from controlled flow in the other direction that consumes the gradient produced. You're trying to make this work by taking in thermal radiation from the CMB, but this also doesn't work, because the CMB is uniform and there's no process cooling the shell's outer surface below the CMB temperature and no process that passively could even in principle.

All that adds up to (A). You cannot define the system in a way that is both self-consistent and functional.

Let's compare with processes that could work:

• You find an asteroid with a liquid ocean and no atmosphere. The liquid evaporates, and you run turbines off the escaping gas. This is Planet X again.
• You find an asteroid hurtling through space at you. You place some device in its way, and extract work from the energy of collision.
• You find a star, and surround it with a Dyson Sphere. The star consumes its own mass to form a hot plasma emitting lots of photons, which you capture and convert to electricity. No problem! You're working off the stored potential of hydrogen to undergo fusion. You consume some of the work to keep the Dyson sphere in place.
• Your Dyson Sphere enclosed star goes supernova and leaves behind a black hole. You hurl damaged pieces of your Dyson Sphere into it, and the (somehow surviving or repaired) remaining pieces extract work from the gamma rays and other radiation given off as matter falls towards the event horizon. No problem - you're consuming the structure and mass-energy of the sphere's matter.
• When you run out of spare Dyson Sphere parts, you've got to use more of that cleverness. The black hole will be colder than the CMB, and will begin gaining mass by absorbing the CMB, and become even colder in the process. I cannot think of a way to use that to do (a very small amount per unit time of) work, but a Sufficiently Advanced Alien might. This works until, eventually, the universe expands and the CMB cools to below the black hole's temperature, after which the black hole's evaporation by Hawking radiation outpaces CMB absorption. Even then you might be able to do work by turning your equipment around and harnessing the Hawking radiation and using the CMB as the heat sink, right up until it finishes evaporating.

So overall: Yes, I can imagine there could be a system that couples some astronomical object to the CMB, absorbing its heat and doing work. No, from within the universe, "we" cannot set up such a system except by finding a pre-existing gradient of structure to extract from, or by doing more work to create such a gradient than we can extract by consuming it.

ablation is much harder than it might sound.

I'm reminded that it's hard to have a mind that questions the stars but never thinks to question the Bible, and much easier (but still hard) to have one savvy enough to lie.

You're sorta talking here about extracting work from an initial pressure differential by converting it to a temperature differential, just like in the Planet X example. 

That would be fine, but it contradicts your post, where you specifically state that everything starts in thermal equilibrium at 5K.  The CMB is still irrelevant and unneeded, and does not provide the kind of T gradient you're claiming. (6) does not work, and (7) is not true.

Agreements

3. Model switching: Having multiple models at different levels of precision and abstraction is useful and switching between them is useful. But, you need to make sure that when you switch, you really make all necessary changes and understand which points you can carry over and which need what kind of reassessment or adjustment. Otherwise you're introducing new and unnoticed errors every time you switch. Doing this well enough to form a useful thought experiment means writing down, as an equation or very precise verbal description, every boundary condition, every initial condition, and every force or law governing the evolution of the system.

4. Complexity: The point is, it is a mistake to consider such details unimportant. You mention keeping the shell in place - in place relative to what? Those "details" mean either some sort of active thrusters that consume work, or some sort of extremely long tethers or pillars that change the set of reference frames with respect to which you're defining the velocity of the particles moving around. They mean your shell and asteroid are not at rest with respect to the reference frame of the CMB, which creates some Doppler shift so the flux is not spatially uniform (turning momentum into a temperature differential, among other things), and also the speeds and frequencies at which the atoms hit the shell and return to the asteroid are not spatially or temporally uniform.

6. It's not about degradation, it's about being able to define such a mechanism at all. You've essentially define a balloon around a thin gas gravitationally bound to an asteroid, such that it has a scale height. If you know where every atom is, then sure, you can intercept the ones falling down and ignore the rest and thereby do work. But then you can't talk about T=5K, because you actually have and are relying on your knowledge of the specific microstate. For you, who somehow has such knowledge, T=0, or at least, T<5K. Otherwise, if you don't have such knowledge, then whatever your try to set up will have to also deal with the atoms moving upwards balancing out the atoms moving downwards, and produce no net work. Solar panels do not have this problem. They have a net flux of high-T sunlight with a known thermal distribution of photon energies coming in to a lower-T environment, and this creates a very predictable theoretically efficiency limit based on the panels' composition. What gets 'degraded' is the sunlight's photon distribution, not the panel's structure.

Questions:

1. I think tightening up your language as described will require a lot of tightening up of your thinking, and make it clearer what is going on. So yes, you should try to do that first and then see where that leaves you. But feel free to ask what you want to ask along the way.
2. No preference.
3. I don't think so, no.

Possible disagreements:

1. It really can't. This does not work or help. See above. You're still trying to call things "small" without comparing their effect size to the other effects you're using them to balance or dismiss. To put it another way: Is there some finite limit to shell radius beyond which you think your model doesn't hold up? What happens as you increase the shell radius without bound, or decrease it to be much small? Which effects scale in which ways, which claims break in which order? If there is no clear upper bound you can reason out in this way, then you could just remove the shell entirely (aka place it at infinity) without changing any implications, which I don't think you believe.
2. This works because of the jar, and does not work without the jar. Without the jar, you're essentially claiming that there is some height above the air at which you can place some apparatus in 'still' air which will nevertheless produce net work by extracting energy from falling gas atoms in a way that is not balanced by the forces being applied to the apparatus by rising gas atoms. This is why the thermal-vs-individual-objects model switch matters. You can see the jar, and choose to act on information you have about the jar, and the cost of acquiring such information is small relative to the work you can get from the jar. This is not true for individual atoms.
3. Ok
   1. Assuming this is about the starting conditions, sure. Not true if you're saying this stays true over time
   2. Ditto
   3. Almost is not entirely. Over time the 'almost' adds up
   4. True, if you set up the initial distribution carefully, but again, drawing conclusions based on this requires a semi-quantitative understanding of what 'very low' means.
   5. Ok, so not graphene as described, then :-) I was assuming physisorption on a low-energy atomically-flat surface with very high and uniform emissivity due to it being a zero bandgap semiconductor. It's been a while but I took a whole class in grad school on low temperature vacuum pumps
   6. Yes, a lot of the thermal energy in solids is phononic. No, your conclusions don't follow, because the real interactions are mediated by specific mechanisms that meaningfully change the result, especially in a thin atmosphere at very low temperature. Classical approximations like heat and temperature are inadequate to predict outcomes here. The phonon density and wavevector distribution, and their effects on momentum and scattering, are quantized and that matters. Example: I once had a conversation with someone who was building quantum computers. They told me about a time they had a piece of metal sitting on a substrate in a very cold vacuum and it just wouldn't cool off, instead staying at the same temperature for days. Turns out the metal wasn't clamped hard enough to the surface it was sitting on. There was essentially a phononic band gap between the metal and the surface that meant the heat just couldn't get out in their setup by conduction without phononic tunneling through a large energy barrier. And it was already too cold for radiative cooling to help, especially since that also would need to account for the phonon momentum distribution since photons have very little momentum. "Very slow atoms bouncing off a very cold surface" is the kind of scenario where you just can't rely on classical approximations.
   7. This is also an instance of insufficiently careful model switching. Are we talking about a gas at rest on average, with a shell positioned at many times the atmosphere's scale height? Or are we talking about atoms which tend to convert radial into orbital motion over time (with large enough mean free path that they can orbit in opposite directions without too many collisions)? In the former case, sure. In the latter case, no. Your original description assumes both, without relative quantification of how large each effect might be.
   8. I think my other response about the tennis ball thought experiment should help clarify this. Again, you're stating multiple assumptions that are approximate and that push in opposite directions, or that can be operationalized in ways that have many different implications.

What you're doing by making the roof more jagged is relaxing what you mean by being 'in the vicinity of height h.' You don't have a precise enough definition for that to be a well-formed question. The jaggedness means the roof's height is not really a single number, it's a range. We haven't discussed either the specific roof shape or the distribution of the balls' trajectories (and thus their horizontal momentum and their kinetic energy distributions). On colliding, a ball will either be deflected net-down or net-up, and in the latter case it will soon hit again, and again, until it deflects sufficiently net-downwards or until gravity reduces its vertical speed to zero. So, sure, when the roof's jaggedness increasing its maximum height by some j<h, then on average the balls will stay in the air longer, and the additional time will mostly be spent between height h and height h+j. And because the vertical speed at height h+j will be lower (even for undeflected balls!) than at height h due to gravity, the fall will start out slower than you'd get from a perfectly elastic deflection from a flat roof at height h. If j is tiny, the roof can't be that jagged, and so the effect on ball distribution will also be tiny. If j is large, with such a shape that many balls can actually make it significantly beyond h, then you can't call it a 'roof at height h' anymore. 

Suppose h=10', and j=1', and the jaggedness is set up in a way that makes the average roof height 10.5'. Then what you're saying amounts to something like: Before the balls were vertically distributed quadratically, like if you'd had them following the usual gravitational parabolic trajectories but just truncated off all the time they'd have counterfactually spent in the top half of a height-2h room. But now the room is ~5% taller, and the balls spend nonzero time in the new top 5% of it, and we're only truncating the top 47.5% of the parabolic trajectory on average, and we have added more ways for the room to interconvert vertical and horizontal moment.  

Obviously I haven't done any simulations or written down any equations to estimate the actual new distribution quantitatively. That would depend on the specific roof shape in ways I can't easily capture in a simple equation (maybe someone else could, but I can't). Even still, rephrased the way I put it above, that's not nearly as surprising as it sounds when you stay vague and handwavy about it. 

I suspect you could define a roof shape and a distribution of horizontal momentum vectors such that the balls would on average  be deflected down faster than in the case of the flat roof.

Now, if I were to make the roof sticky instead of jagged, then sure, the balls spend more time there right at height h. But then the roof is absorbing the momentum and kinetic energy, producing heat in the process.

I enjoy things like this, feel free.