Second law of thermodynamics: Spontaneous cold-to-hot heat transfer in a nonchaotic medium

It has long been known that, fundamentally different from a large body of rarefied gas, when a Knudsen gas is immersed in a thermal bath, it may never reach thermal equilibrium. The root cause is nonchaoticity: as the particle-particle collisions are sparse, the particle trajectories tend to be independent of each other. Usually, this counterintuitive phenomenon is studied through kinetic theory and is not considered a thermodynamic problem. In current research, we show that if incorporated in a compound setup, such an intrinsically nonequilibrium behavior has nontrivial consequences and cannot circumvent thermodynamics: cold-to-hot heat transfer may happen spontaneously, either continuously (with an energy barrier), or cyclically (with time-dependent entropy barriers). It allows for production of useful work by absorbing heat from a single thermal reservoir without any other effect. As the system obeys the first law of thermodynamics, it breaks the boundaries of the second law of thermodynamics.