  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, the refrigeration statement and the
heat-engine statement of the second law of thermodynamics cannot be applied.
The basic principle of maximum entropy is adhered to.
