The current theory is based on classical hamiltonian mechanics, but I think the theorems apply whenever you have a markovian coarse-graining. Fermion doubling is a problem for spacetime discretization in the quantum case, so the coarse-graining might need to be different. (E.g. coarse-grain the entire hilbert space, which might have locality issues but probably not load-bearing for algorithmic thermodynamics)
On outside view, quantum reduces to classical (which admits markovian coarse-graining) in the correspondence limit, so there must be some coarse-graining that works
The current theory is based on classical hamiltonian mechanics, but I think the theorems apply whenever you have a markovian coarse-graining. Fermion doubling is a problem for spacetime discretization in the quantum case, so the coarse-graining might need to be different. (E.g. coarse-grain the entire hilbert space, which might have locality issues but probably not load-bearing for algorithmic thermodynamics)
On outside view, quantum reduces to classical (which admits markovian coarse-graining) in the correspondence limit, so there must be some coarse-graining that works