Stationary flows in quantum dissipative closed circuits as a challenge to thermodynamics

An experimentally inspired model is constructed and rigorously solved from the Hamiltonian level where a dc circular spontaneous flow exists in absence of a magnetic field, irrespective of presence of dissipation causing otherwise proper relaxation. The flow causes a spontaneous unidirectional transfer of heat from one bath to another one, even against temperature step. This is what is explicitly forbidden by the Clausius form of the Second law of thermodynamics. The unidirectionality of the flow is caused by that of spontaneous processes known to bear this property since their introduction by Einstein. The model slightly improves the previous one (\v{C}\'{a}pek & Sheehan 2002), describes a realistic plasma system for which experimental results violating the second law were announced, and the result obtained fully supports the experimental conclusions (Sheehan 1995). Analytical proof of the violation is supported by numerical results. All mathematical details are exposed, two fully independent types of mathematical arguments behind starting equations are invoked, and no approximations that could be made responsible for the striking conclusions are used. It shows how the physics beyond the Second law is still little understood.