Giant enhancement of transport driven by active fluctuations: impact of inertia

TL;DR

The paper investigates how inertia affects the giant transport enhancement observed for a Brownian particle driven by active Poisson shot noise in a periodic potential. Using a dimensionless inertial Langevin framework with a skew-normal amplitude distribution for active bursts, the authors map how the long-time drift $\langle v\rangle$ changes relative to the overdamped case and the free particle as functions of spiking rate $\lambda$, barrier height $\varepsilon$, and amplitude variance $\sigma^2$. They identify four regimes—strengthening, weakening, destructive, and inertia-induced constructive transport—highlighting that inertia can both suppress and enhance the effect, with the variance $\sigma^2$ acting as a key determinant. The results extend the understanding of non-equilibrium transport in active matter, offering predictions relevant to nanoscale devices and living cells, and suggesting experimental platforms such as Josephson junctions and optically trapped colloids for validation.

Abstract

Recently, a paradoxical effect has been demonstrated in which transport of a free Brownian particle driven by active fluctuations in the form of white Poisson shot noise can be significantly enhanced when it is additionally subjected to a periodic potential. This phenomenon can emerge in an overdamped system, but it may also be inertia-induced. Here, we considerably extend previous studies and comprehensively investigate the impact of inertia on the effect of free transport enhancement observed in the overdamped system. We detect that inertia can not only induce this phenomenon, but depending on a parameter regime, it may also strengthen, weaken, or even destroy it. We exemplify these different scenarios and explore the parameter space to identify the corresponding regions where they emerge. The variance of the active fluctuations amplitude distribution is a key determinant of the inertia influence on the effect of free transport amplification. Our results are relevant not only for microscopic physical systems but also for biological ones, such as, e.g., living cells, where fluctuations generated by metabolic activities are active by default.

Figures (6)

• Figure 1: The average velocity $v_\gamma$ of an overdamped ($m = 0$) Brownian particle in a periodic potential $U(x)$ and driven by active fluctuations $\eta(t)$ as a function of their spiking rate $\lambda$ and variance $\sigma^2$. Other parameters are the mean bias $\langle \eta(t) \rangle = \lambda \zeta = 1$, skewness $\chi = 0.99$ and half of the potential barrier height $\varepsilon = 250$. The regions where the average velocity of the particle dwelling in the periodic potential is larger than for the free particle, i.e. $v_\gamma > v_0$, are marked with grey $\blacksquare$ color and the white background represents regions without the enhancement.
• Figure 2: The average velocity $v_m$ of an inertial ($m \neq 0$) Brownian particle in a periodic potential $U(x)$ and driven by active fluctuations $\eta(t)$ as a function of their spiking rate $\lambda$ and variance $\sigma^2$. Other parameters are the mean bias $\langle \eta(t)\rangle=\lambda \zeta=1$, skewness $\chi=0.99$, and half of the potential barrier height $\varepsilon=250$. The parameter sets are marked with the corresponding color depending on the influence of the inertia on the average velocity: strengthening $\blacksquare$$v_m > v_\gamma > v_0$, weakening $\blacksquare$$v_0 < v_m < v_\gamma$, destructive $\blacksquare$$v_m < v_0 < v_\gamma$ or constructive (inertia-induced) $\blacksquare$$v_\gamma < v_0 < v_m$. In panels (a), (b) and (c), the particle mass reads $m=0.01$, $m=0.1$ and $m=1$, respectively.
• Figure 3: An illustration of the negative influence of inertia on the effect of free transport enhancement. The average velocity $\langle v \rangle$ of the Brownian particle driven by active fluctuations $\eta(t)$ as a function of the periodic potential $U(x)$ barrier height $\varepsilon$ for different values of mass $m$ is shown in panel (a). In plot (b), the same quantity is depicted versus $m$ and for different barrier heights $\varepsilon$. Other parameters read $\langle \eta(t)\rangle= \lambda \zeta=1$, variance $\sigma^2=2$, skewness $\chi=0.99$. In panel (a) the barrier height is $\varepsilon=250$ and in (b) the spiking rate is $\lambda=50$.
• Figure 4: An illustration of the positive influence (strengthening) of inertia on the effect of free transport enhancement. The average velocity $\langle v \rangle$ of the system as a function of the barrier height $\varepsilon$ for different masses $m$ (panel (a)) and versus mass $m$ and various barrier heights (panel (b)). Other parameter read $\langle \eta(t) \rangle=\lambda \zeta=1$, variance $\sigma^2=50$, skewness $\chi=0.99$. In panel (a), the barrier height is $\varepsilon=250$ and in panel (b), the spiking rate is $\lambda=5$.
• Figure 5: An illustration of the positive influence (constructive) of inertia on the effect of free transport enhancement. The average velocity $\langle v \rangle$ of the system as a function of the barrier height $\varepsilon$ for different masses $m$ (panel (a)) and versus mass $m$ and various barrier heights (panel (b)). Other parameter read $\langle \eta(t)\rangle=\lambda \zeta=1$, variance is $\sigma^2=20$, skewness $\chi=0.99$. In panel (a), the barrier height is $\varepsilon=250$ and in panel (b), the spiking rate is $\lambda=5$.