Mass separation under zero effective average temperature difference

Separation of particles with different masses at the micro- and nanoscales plays a crucial role across various fields, whereby the Ludwig–Soret effect serves as an important mechanism. This effect is typically induced by a stable temperature gradient maintained through a fixed temperature difference. In this paper, using a one-dimensional soft-core bi-component atomic gas model, we demonstrate that complete mass separation due to the Ludwig–Soret effect can occur even under a zero effective average temperature difference. Contrary to the case with a sufficiently large fixed temperature difference, this separation is characterized by the heavy particles accumulating in the low-temperature region, while the light ones accumulating in the high-temperature region. Complete mass separation is facilitated by an increase in the amplitude of the time-varying temperature, and also by a higher finite potential barrier that dictates the interaction between particles. Both a higher potential barrier and a lower average environmental reference temperature require longer integration times to ensure steady-state results. The upper bound of the average environmental reference temperature that enables complete mass separation increases linearly with the potential barrier. When one mass is held fixed while the other is reduced or increased relative to the fixed mass, this upper bound decreases nonlinearly. This separation may stem from probabilistic differences for different masses inherent in the statistical heat bath itself. Our results offer novel insights into controlling mass separation under dynamic nonequilibrium conditions.