Thank you for your very thoughtful note! What is the export of Trinidad to which you refer in your footnote 6 — natural gas?

If we want to compare the carrying capacity of Spaceship Earth under solar power in the future and the past, I think it behooves us to consider the whole sunbeam-to-wheels efficiency, or sunbeam-to-hooves, as the case may be. It's true that photosynthesis is about 1–3% efficient (I think beema and sugarcane can approach 4% at times), but typical crop yields are closer to 0.3 W/m² [1], which is an efficiency of 0.1% if sunlight averages 300 W/m². Also, muscles are not perfectly efficient, and animals can't spend 100% of their energy input on their muscles; they have to spend some of it on digestion, homeostasis, reproduction, and — though this may be redundant — rest. So if draft animals are 20% efficient [0] and food production by photosynthesis is 0.1% efficient, then the total sunlight-to-hooves efficiency of plowing with oxen, horses, or by pulling the plow by hand, is in the neighborhood of 0.02%.

By contrast, low-cost photovoltaic panels are 16% efficient, as you say; electric motors and generators are typically about 90% efficient in combination, and the rest of the electrical system is typically about 90% efficient, as long as no batteries or high-voltage transmission are required. This gives a sunlight-to-wheels efficiency of about 13% for the best realistic case of solar, about 600 times better than corn-fed oxen. (Multijunction cells could push that up to 33% or so, but they're far too expensive with current production techniques.)

However, it might prove difficult to refine silicon in the case of a collapse of the post-1970s industrial infrastructure, so perhaps it is best not to calculate based on photovoltaic panels. A more conservative low-tech case is, as you imply, a CSP-driven steam engine like Frank Shuman's 1912 Sun Power Company power station Solar Engine One, which I mentioned in https://news.ycombinator.com/item?id=22363678 and which reputedly achieved about 4% efficiency [2]. If applied to Watt's 3%-efficient vacuum engine driving a generator, a solar thermal collector with an easily accessible efficiency of 50% would produce sunlight-to-wheels efficiency of about 1.2% — not great, but still 60 times better than oxen or corn-fed farm boys.

So there are, I think, excellent reasons to believe that solar energy could sustain current levels of human population on Spaceship Earth, even after a hypothetical systemic collapse.

As for proposed energy technologies with efficiencies below 0, these would be perpetual-motion machines: if applied to a 100-watt load, an engine of efficiency -10% would supply the load with 100 watts while consuming -10 watts, which is to say, producing 10 watts in some other form, perhaps electricity. I do not expect to see many of these. Perhaps this was not what you meant?

I will respond separately to your comments about materials recycling.

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[0] https://www.forbes.com/sites/kevinmurnane/2016/07/18/fueling... Tour de France riders eat 6000 to 8000 kcal per day (25–35 MJ in modern units, 300–400 W), 30% of which is just their basal metabolism, while racing 6 hours per day at about 400 watts of power output. That's about 30% cornbread-to-wheels efficiency, but it omits the power usage of reproduction, growth, and homeostasis — racers can't train year-round at Tour-de-France intensity levels without dying, nor can they do it while pregnant or growing out of childhood. Even during the race, most days are less than 6 hours of racing, and there are two official "rest" days with no racing at all.

[1]
http://www.worldofcorn.com/#us-average-corn-yield-metric
says US corn yield is 11 tonnes/hectare, presumably per year. If corn is the standard 15.5% moisture and the rest carbohydrate and protein at 4 kcal/g — not precisely correct, but close enough — that's about 0.5 W/m².
https://apps.fas.usda.gov/psdonline/circulars/production.pdf
table 04 says the world produced 1079.9 million metric tons of corn in the 2017/18 year on 192.12 million hectares, for a yield of 5.62 tonnes/hectare, so that seems reasonable, but that's only ¼ W/m².

[2] https://www.scientificamerican.com/article/power-from-sunshi... is an article Shuman wrote before building it. The actually built plant was reported to produce only about 50 to 60 horsepower when the sun was shining; according to M. Ragheb's Solar Thermal Power and Energy Storage Historical Perspective, it had five 62 m × 4 m troughs at 7.6 m spacing, totaling 248 m² of collector. However, this would collect 248 kW of insolation, implying an efficiency of 15–18%, which is implausibly high for a steam engine. Ragheb also, contradictorily, reports that it was 4% efficient. I suspect a unit conversion error.