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Owen Lynch (Nov 23 2021 at 17:36):Linear Irreversible Thermodynamics, or "LIT" as it is called by Schnakenberg, might be a good toehold for categorification. Putting this here so I remember, might circle back to this in a bit.
Owen Lynch (Nov 23 2021 at 17:37):It may end up almost totally isomorphic to resistor networks, the only added complication is that there are different "types" of things that can be transferred instead of just electrical current.
Owen Lynch (Nov 23 2021 at 17:40):
John Baez (Nov 23 2021 at 17:49):Okay, yeah we might do this as part of a more general nonlinear theory. It should be close to resistor networks - but even closer to detailed balanced Markov processes, which we dealt with using categories here:
The detailed balance condition is necessary to get thermodynamically reasonable behavior from a Markov process: namely, no net flows around loops in equilibrium. We figured out how to reduce detailed balanced Markov processes to circuits of resistors.... and then use Brendan's and my earlier work on those.