One response brings up the (un)decidability of determining if a physical system's ground state is separated from the rest of its spectrum: > And there are stil

One response brings up the (un)decidability of determining if a physical system's ground state is separated from the rest of its spectrum: > And there are still cases going on today where undecidability results are of broad interest to those outside of logic. For example, the "spectral gap problem" in physics asked whether, given a description of a physical system, whether that system requires a minimum amount of energy to nudge it out of its ground state, or whether arbitrarily small amounts of energy can nudge it out of its ground state. This was proven to be undecidable in 2015, basically telling physicists that a theoretical problem of theirs, motivated entirely by physical considerations, is hopeless in full generality. Well that sucks.[1] But I think it's cool that theoretical physics and theoretical computer science seem to meet together in these low places. Information has thermodynamic consequences and vice versa. [1] https://arxiv.org/abs/1502.04135 https://arxiv.org/abs/1502.04135