H-Theorem and Local Violation of the Second Law of Thermodynamics in Quantum Physics

The arrow-of-time dilemma, how the irreversibility of the world around us emerges from the time-symmetric fundamental laws of physics, remains a puzzle. Boltzmann reconciled irreversibility with Newton’s laws, using the molecular chaos hypothesis. Von Neumann’s formulation of the quantum H-theorem and the quantum origin of irreversibility allowed for dropping this hypothesis but invoked the macroscopic measurement procedure. Recent developments suggested the solely quantum origin of irreversibility, underlining the key role of the quantum entanglement, yet a thorough understanding of arrow-of-time formation remains unsettled. Here we make a first step towards the unraveling the origin of the arrow of time and formulate the quantum H-theorem in terms of physical observables. We discuss manifestations of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be locally violated. We introduce a concept of the Quantum Maxwell Demon and demonstrate how does it help to design the perpertual motion machine of the second kind.