Stationary states of relaxed open systems

Several different first-principle theories that are all potentially able to determine the long-time limit of states of open quantum systems are examined and critically compared in the formal second-order approximation. Because of a big parameter of the problem (increasing time), formal mathematical solution behind this second order exists just in the form of practically inapplicable formulae. Fortunately, in the second order, physical arguments could be given leading to a unique conclusion.