Local Detailed Balance Invariant States of Markov Generators of Low Density Limit

We introduce the notion of local detailed balance for low density limit generators of quantum Markov semigroups and explore the consequences of this condition on the structure of the corresponding set of invariant states. The local detailed balance condition allows us to include the case of degenerate reference Hamiltonian and due to this degeneracy, we can compute nonequilibrium invariant states by combining the local detailed balance with generic, quasi-generic and [Formula: see text]-generic conditions, obtaining LDL Markov generators with pure invariant states.