Perturbation theory for open quantum systems

Two methods is commonly used for derivation of master equations in theory of open quantum systems and quantum thermodynamics: so-called global and local approaches. The global approach has a mathematical justification, but is often inapplicable in practice due to its complexity. So, the so-called local approach is often used, which heuristic and does not take into account the interaction of system elements with each other. Over the last few years, a number of papers were published with the statements that the local approach contradicts the second law of thermodynamics (the law of entropy growth). In our paper we show that the local approach also can be mathematically justified on the basis of the perturbation theory. We derive corrections to the local approach and proof that the correct use of the perturbation theory does not lead to contradictions with the second law of thermodynamics.