Noether’s theorem is an actual theorem. You will find it formulated and proved in textbooks on mathematical physics, and indeed was formulated and proved at its original publication.
Is the Free Energy Principle a theorem? I have spent a deal of time studying the FEP primary sources, trying to grasp the mathematics, but I have not yet found the sort of text that I described above. This paper, from its title, is where I would expect to find what I am looking for, but there is little mathematical argument there, with not even a mention of the Langevin equations, Fokker-Planck equations, and Non-Equilibrium Steady States that some other sources go into. Instead, the FEP is formulated verbally as e.g. “all the quantities that can change; i.e., that are owned by the system, will change to minimise free energy”.
Has anyone written the sort of textbook exposition for the FEP that is routine for things like Noether’s theorem? Or if the FEP is a different sort of thing, what sort of thing is it, that is “unfalsifiable” yet not a mathematical truth?
Noether’s theorem is an actual theorem. You will find it formulated and proved in textbooks on mathematical physics, and indeed was formulated and proved at its original publication.
Is the Free Energy Principle a theorem? I have spent a deal of time studying the FEP primary sources, trying to grasp the mathematics, but I have not yet found the sort of text that I described above. This paper, from its title, is where I would expect to find what I am looking for, but there is little mathematical argument there, with not even a mention of the Langevin equations, Fokker-Planck equations, and Non-Equilibrium Steady States that some other sources go into. Instead, the FEP is formulated verbally as e.g. “all the quantities that can change; i.e., that are owned by the system, will change to minimise free energy”.
Has anyone written the sort of textbook exposition for the FEP that is routine for things like Noether’s theorem? Or if the FEP is a different sort of thing, what sort of thing is it, that is “unfalsifiable” yet not a mathematical truth?