Absolute negative mobility in a one-dimensional overdamped system driven by active fluctuations

Abstract

Absolute negative mobility (ANM) is one of the most paradoxical transport phenomena in which a setup moves on average in a direction opposite to the applied force. According to the state of the art a minimal system exhibiting this effect in a one-dimensional dynamics involves an inertial particle subjected to a constant bias when dwelling in a nonlinear symmetric periodic potential in a nonequilibrium} and nonstationary state generated by an external driving. In this work we remarkably reduce its complexity and show that it may occur in a system composed of an overdamped particle in piecewise linear symmetric periodic potential in an equilibrium state provided that it is driven by active fluctuations in the form of white Poisson shot noise. Our result may help to explain exotic transport behavior emerging in biological cells where dynamics is typically overdamped and assisted by active fluctuations derived from various metabolic activities. It can be also exploited for effective separation strategies in a microscopic world thus transforming fluctuations from a nuisance into a functional resource.

Figures (8)

• Figure 1: Evolution of a Brownian particle dwelling in a piecewise linear potential $U_l(x)$ driven by a single $\delta$-spike of active fluctuations $\eta(t)$. $\Delta x_P$ stands for a distance covered by the particle due to the arrival of $\delta$-spike whereas $\Delta x_R$ represents the displacement because of the relaxation towards the potential $U_l(x)$ minimum. Two situations are exemplified: (i) the rare spiking regime $\lambda \to 0$, (ii) the case of finite $\lambda$.
• Figure 2: The average velocity $\langle v \rangle$ of a Brownian particle as a function of the average bias $\langle \eta(t) \rangle = \lambda \zeta$ of active fluctuations depicted for different values of the mean amplitude $\zeta$. Other parameters read the barrier height $\varepsilon = 100$, variance $\sigma^2 = 20$ and skewness $\chi = 0.99$. The solid and dashed lines correspond to piecewise the linear $U_l(x)$ and cosine $U_c(x)$ potential, respectively.
• Figure 3: The average velocity $\langle v\rangle$ as a function of average bias $\langle \eta(t)\rangle$ of active fluctuations for different values of barrier height $\varepsilon$. The mean amplitude is $\zeta=0.01$. Other parameters are the same as in Fig. \ref{['fig:1']}. The solid and dashed lines correspond to the piecewise linear $U_l(x)$ and cosine $U_c(x)$ potential, respectively.
• Figure 4: The average relaxation distance $\langle \Delta x_R \rangle|_{\lambda \to 0}$ in the piecewise linear potential $U_l(x)$ for the limit of rare $\delta$-spikes (see Eq. (\ref{['eq:x_R_0']})) as a function of the mean amplitude $\zeta$ of active fluctuations $\eta(t)$. The parameters are the same as in Fig. \ref{['fig:1']}.
• Figure 5: The average velocity $\langle v \rangle$ versus the mean bias $\langle \eta(t)\rangle =\lambda \zeta$. Comparison between the precise numerical simulations of the dynamics (\ref{['model']}) and the approach Eq. (\ref{['eq:av_v']}) with the average relaxation distance $\langle \Delta x_R \rangle$ given by Eq. (\ref{['eq:x_R_0']}) and Eq. (\ref{['eq:x_R_ran']}). Other parameters are the same as in Fig. \ref{['fig:1']}.