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Underground dwarven (and other) civilizations are a staple of fantasy worlds. The obvious question (what do these people eat?) is rarely answered.

As an explanation, I considered a food chain based in some kind of organism that feeds on thermal energy. These organisms would inhabit volcanic regions, exploiting the temperature gradient to free up energy, which could then be used to synthesize complex sugars, much like earth plants. The actual atoms used could be extracted from water and either carbon-rich minerals or air. This 'plant' would probably have thin snaky roots to cover a wider range of temperatures and better extract the required minerals.

Are such organisms at all plausible, biologically? Would they be able to produce enough energy to support at least a small ecosystem? Could they be cultivated on large-scales, assuming that this world has weirdly favorable cave/volcano systems that provide them with a lot of habitat?

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Hydrothermal vents already work on using the energy supplied by volcanic activity and are the base of quite large food chains. However what the organisms use is not the heat, but rather the chemical energy available thanks to the chemicals contained in the outflowing water.

It would be difficult for a microorganism to have two places at largely different temperature to use for creating useful work, while it's more easy to have access to chemicals and use them to supply biotic reactions.

L.Dutch
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    +1 for something I didn't consider when I thought of the vents -- where there's large temperature gradients, different molecules are stable at one temperature and unstable at another, creating this opportunity to use chemical energy. This also has a neat advantage that it can leverage chemicals which were made in unreasonably hot areas where life cannot exist (like right next to magma), and those chemicals can flow to a cooler area (still hot but within the life-supporting ranges of temperatures). This opens tons of doors for a food web. – Cort Ammon Oct 18 '22 at 13:47
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Radiotrophs could work instead of your heat-eaters. They basically use radiation to feed themselves, so they could grow in areas with pitchblende (contains radioactive materials).

https://en.wikipedia.org/wiki/Radiotrophic_fungus