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

It is well known that, when immersed in a thermal bath, a Knudsen gas cannot relax to thermal equilibrium. The root cause is nonchaoticity, i.e., the lack of extensive particle-particle collisions. Usually, this counterintuitive phenomenon is not considered a thermodynamic problem. Here 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 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.