Engineering Ratchet-Based Particle Separation via Shortcuts to Isothermality

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 $\tau$, we find in the slow-driving regime that the average particle velocity $\text{Bar}{v}_s\propto (1-D\mathrm{/}{D}^{\ast }){\tau }^{-1}$, indicating that particles with different diffusion coefficients $D$ can be guided to move in distinct directions with a preset $D^{\ast }$. Furthermore, we reveal that there exists an extra energetic cost with a lower bound $W_{\mathrm{e}\mathrm{x}}^{(\mathrm{m}\mathrm{i}\mathrm{n})}\propto {\mathcal{L}}^2\text{Bar}{v}_s$, alongside a quasi-static work consumption. Here, $\mathcal{L}$ 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 $W_{\mathrm{e}\mathrm{x}}^{(\mathrm{m}\mathrm{i}\mathrm{n})}$) 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.