On the second law of thermodynamics: A global flow spontaneously induced by a locally nonchaotic energy barrier

It is well known 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 boundaries of the second law of thermodynamics where Boltzmann’s H-theorem does not apply, there may also be 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.