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This leads me to strongly suspect that the thermodynamic properties of life are, at the very least, a necessary condition for a system's ability to support consciousness
It still sounds like a non-sequitur to me. Is there some non-trivial minimum time an entity must continue to exist before it can be considered conscious?
Biological organisms do have sophisticated metabolism and repair capabilities, but these eventually fail and the organism dies. Sometimes they fail very early due to inherent faults. A house mouse can live for about 4 years, but may dies much earlier. If we can consider it to have a rudimentary consciousness over that lifespan, would it not count as consciousness if it only lived for one month? We can build complex electronic machines that function reliably for many years. They can find suitable power sources, and we can give them multiple redundancy and reconfigurablility to make them more resilient, but their repair facilities aren't as sophisticated as those of living things, but why is this a problem for supporting consciousness?
What is the essential connection you think you see between the thermodynamics of life and consciousness?