Giant Acceleration of Diffusion in Soft Matter Potential

Diffusion of Brownian particles in the tilted periodic potential, usually referred to the washboard potential (WBP), is a well-known model to describe physical systems out of equilibrium. Considering that the biological medium is flexible and thermally fluctuating, a new model, namely the soft matter potential (SMP), is proposed to describe the biological medium. Compared to the washboard potential (WBP), SMP allows Brownian particles to actively modify the structure of the biological medium. Brenner's homogenization theory is applied to predict the diffusivity and velocity of Brownian particles driven by external forces in SMP. Thermodynamic uncertainty relation (TUR) is analyzed for Brownian particles in SMP. It is found that, compared to WBP, Brownian particles in SMP require a lower energy cost $\langle q \rangle$ to achieve accuracy $\mathcal{A}$, i.e. Brownian particles in SMP have higher transport efficiency when driven by external forces.