Microscopic particle separation plays vital role in various scientific and
industrial domains. In this Letter, we propose a universal non-equilibrium
thermodynamic approach, employing the concept of Shortcuts to Isothermality, to
realize controllable separation of overdamped Brownian particles. By utilizing
a designed ratchet potential with temporal period Ο, we find in the
slow-driving regime that the average particle velocity
\Bar{v}_s\propto\left(1-D/D^*\right)\tau^{-1}, indicating that particles with
different diffusion coefficients D can be guided to move in distinct
directions with a preset Dβ. Furthermore, we reveal that there exists an
extra energetic cost with a lower bound
W_{\rm{ex}}^{(\rm{min})}\propto\mathcal{L}^{2}\Bar{v}_s, alongside a
quasi-static work consumption. Here, L is the thermodynamic length
of the driving loop in the parametric space. We numerically validate our
theoretical findings and illustrate the optimal separation protocol (associated
with Wex(min)β) with a sawtooth potential. This study
establishes a bridge between thermodynamic process engineering and particle
separation, paving the way for further explorations of thermodynamic constrains
and optimal control in ratchet-based particle separation.Comment: 5 pages, 3 figures + Supplemental Materials (10 pages, 4 figures).
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