Transport enhancement and entropic stochastic resonance of Brownian particles in symmetric deformable channels

We investigated in this work the transport enhancement and entropic stochastic resonance of Brownian particles in symmetric, corrugated, deformable channels. The diverse geometries of our channel, shown by the widening or narrowing of the potential wells and barriers, significantly affect the dynamics of Brownian particles when mass is included. We used the boundary reflection condition to retain the particles inside the channel. We have shown that under suitable parameter conditions in our systems, the channel’s symmetry can be observed in results such as the evolution of the channel’s potential barrier in relation to the biharmonic force exerted on the particles, as well as the mean first passage time and spectral amplification where entropic stochastic resonance occurs. With the rise in noise intensity, spectral amplification exhibits non-monotonic behavior, indicating the occurrence of entropic stochastic resonance. By modulating the amplitudes of the harmonics $A_0$, the frequency of the driving biharmonic signal $\omega$, the scale ratio of the second harmonic $ϵ$, the phase lag of the two signals $\varphi$, and the configuration of the deformable channel, we can discern a reverse average velocity and an optimization of effective diffusion for particular particle masses. It is essential to emphasize that particle transport via channels encompasses a diverse array of processes, including osmosis, ionic current through ionic channels, particle separation, and the modeling of dilute mixtures of microscopic fragments, among others.