  People are well aware that, inherently, certain small-scale nonchaotic
particle movements are not governed by thermodynamics. Usually, such phenomena
are studied by kinetic theory and their energy properties are considered
"trivial". In current research, we show that, beyond the boundary of the second
law of thermodynamics where Boltzmann's H-theorem does not apply, there are
also large-sized systems of nontrivial energy properties: when the system is
isolated, entropy can decrease; from a single thermal reservoir, the system can
absorb heat and produce useful work without any other effect. The key concept
is local nonchaoticity, demonstrated by using a narrow energy barrier. The
barrier width is much less than the nominal particle mean free path, so that
inside the barrier, the particle-particle collisions are sparse and the
particle trajectories tend to be locally nonchaotic. Across the barrier, the
steady-state particle flux ratio is intrinsically in a non-Boltzmann form. With
a step-ramp structure, the nonequilibrium effect spreads to the entire system,
and a global flow is generated spontaneously from the random thermal motion.
The deviation from thermodynamic equilibrium is steady and significant, and
compatible with the basic principle of maximum entropy. These theoretical and
numerical analyses may shed light on the fundamentals of thermodynamics and
statistical mechanics.
