It is well known that, inherently, certain nonchaotic particle movements cannot reach thermodynamic equilibrium (Section 2). Usually, they are small-scale and their behaviors are “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 (Section 3). 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, particle-particle collision is 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. Although the direct experimental realization of the model may be difficult, the theoretical and numerical analyses could shed light on the fundamentals of thermodynamics and statistical mechanics.