Shortcuts to isothermality applied to ratchet potentials enable separation of Brownian particles by diffusion coefficient D via velocity scaling v_s ∝ (1 - D/D*) / τ in the slow-driving limit, plus a minimal extra work cost ∝ L² v_s.
There may exist different trajectories leading to the same particle flux but have different energy cost
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Engineering Ratchet-Based Particle Separation via Shortcuts to Isothermality
Shortcuts to isothermality applied to ratchet potentials enable separation of Brownian particles by diffusion coefficient D via velocity scaling v_s ∝ (1 - D/D*) / τ in the slow-driving limit, plus a minimal extra work cost ∝ L² v_s.