Ornstein-Uhlenbeck information particle: A new candidate of active agent

TL;DR

This work investigates how an information engine can induce active propulsion in a Brownian particle by modulating an attached Ornstein–Uhlenbeck bath, replacing constant self-propulsion with OU-driven feedback (OUIP) and comparing it to a standard self-propelled particle (SPP). Extending from 1D to 2D, the authors show OUIP supports two distinct motion modes—a slow diffusion-like regime and a fast traveling regime—whose balance is controlled by inertia and the OU-bath fluctuation strength $\tilde{A}$, yielding a tunable net propulsion along the particle's orientation, $\langle v_{\parallel} \rangle$. The key contributions include (i) a dimensionless, feedback-driven OUIP model with velocity-threshold based OU-bath switching, (ii) demonstration of two-mode velocity distributions and inertia-tunable behavior, and (iii) demonstration that OUIP can realize a wide range of effective self-propulsion speeds. The findings highlight OUIP as a promising active-agent candidate for studying non-equilibrium dynamics and guiding bioinspired engineering, with potential applications in modeling run-and-tumble dynamics and other complex motility patterns.

Abstract

An information particle can acquire active-like motion through transforming the information entropy into effective self-propulsion velocity/force using the attached information engine. We consider an underdamped Brownian particle additionally driven by either a constant self-propulsion force or an information engine using Ornstein-Uhlenbeck (OU) bath feedback control, such particles are called self-propelled particle (SPP) or OU information particle (OUIP). Compared to the widely-investigated SPP, the OUIP shows a significant different dynamical pattern, including two types of moving mode: a slow-speed diffusion mode and a high-speed traveling mode. The specific evolution of OUIP can be adjusted flexibly between such two modes through the inertial effect, thus acquiring a rich and non-trivial motion behavior. By tuning the strength of fluctuation of the OU bath, a wide range of net velocity can be achieved for OUIP. We highlight that OUIP could be an exceptional candidate for active agent.

Figures (5)

• Figure 1: (a) The velocity distribution probability of SPP in the orientation direction, where $\tilde{U}_0 = 18$ and $\tilde{M}=1$. Inset: The time evolution of velocity. The red lines denote the average velocity of SPP along its orientation direction. (b) The velocity distribution probability of OUIP along its orientation direction in polar coordinates, where $(\beta_1, \beta_2) = (10, 0.1)$, threshold velocity $\tilde{v}_0 = 0$, measurement time interval $\tilde{\tau}_{\rm{m}} = 10 \Delta \tilde{t}$ with $\Delta \tilde{t} = 0.001$, and the fixed parameters are $\tilde{A} = 63$, $\tilde{\tau}_{\rm{a}} = 1$ and $\tilde{M}=1$. Inset: The time evolution of velocity. The red solid lines denote the average velocity of OUIP along its orientation direction. (c) The distribution probability of velocity $P(\tilde{v}_x)$ of SPP and OUIP on $x$-axis in Cartesian coordinate system. The parameters of particles are same as in (a) and (b).
• Figure 2: The motion characteristics (a-b) and inertial-effect (c) of selected representative OUIP. (a) The velocity distribution $P(\tilde{v}_{\parallel})$ of OUIP in the orientation direction of particle. The red solid vertical line denotes the average velocity of OUIP along its orientation direction. The blue and green solid lines are Gaussian fittings. (b) The velocity distribution $P(\tilde{v}_x)$ of OUIP on the $x$-axis of Cartesian coordinate in space. The dashed blue and green lines are stretched exponential fittings ($P(\tilde{v}_x) \sim \exp(-(\vert \tilde{v}_x/v_c \vert)^{\alpha})$ with $\alpha \sim 1.445$ and $1.65$, respectively). (c) The velocity distribution probability $P(\tilde{v}_{\parallel})$ of OUIP under various inertia effects that controlled by reduced mass $\tilde{M}$. The parameters of selected OUIP are $(\beta_1, \beta_2) = (10, 0.1)$, threshold velocity $\tilde{v}_0 = 15$, measurement time interval $\tau_{\rm{m}} = 10 \Delta \tilde{t}$ with $\Delta \tilde{t} = 0.001$, and the fixed parameters are $\tilde{A} = 100$ and $\tilde{\tau}_{\rm{a}} = 1$. The reduce mass in (a) and (b) is fixed as $\tilde{M} = 0.2$.
• Figure 3: Obtaining net average velocity $\langle \tilde{v}_{\parallel} \rangle$ of OUIP by tuning the value of $\tilde{A}$. Here, we choose $(\beta_1, \beta_2) = (10, 0.1)$, threshold velocity $\tilde{v}_0 = 0$, measurement time interval $\tilde{\tau}_{\rm{m}} = 10 \Delta \tilde{t}$ with $\Delta \tilde{t} = 0.001$, the fixed parameters are $\tilde{\tau}_{\rm{a}} = 1$ and $\tilde{M} = 1$.
• Figure 4: The velocity distribution probability of Brownian particle with/without the Ornstein-Uhlenbeck (OU) noise bath attached. (a-b) The distribution probability of velocity of Brownian particle (BP) and active OU particle (AOUP) on the orientation direction in polar coordinate (a) and on the $x$-axis in Cartesian coordinate (b). The 'No OU bath attached' case corresponds to the Brownian particle (BP). The parameter $\beta$ is set to be 0.1 and 10, respectively. Other parameters of AOUP are $\tilde{A}=100$, $\tilde{\tau}_{\rm{a}} = 1$, and $\tilde{M} = 1$. The solid lines are Gaussian fits. (c-d) The velocity distribution probability of AOUP under various inertia effects ($\tilde{M}$). The fixed parameters are $\beta = 10$, $\tilde{A}=100$, and $\tilde{\tau}_{\rm{a}} = 1$. The solid lines are Gaussian fits. The black, red and blue dashed lines in (d) are stretched exponential fits $P(\tilde{v}_x) \sim \exp({-|\tilde{v}_x/v_c|^{\alpha}})$ with $\alpha \sim 1.83$, $1.57$, and $1.15$, respectively. Inset: the value of $\alpha$ as a function of $\tilde{M}$.
• Figure 5: The obtaining net average velocity $\langle \tilde{v}_{\parallel} \rangle$ of OUIP as a function of $\tilde{A}$ under the reduced mass $\tilde{M} = 0.1$ and $10$, respectively. Here, we choose $(\beta_1, \beta_2) = (10, 0.1)$, threshold velocity $\tilde{v}_0 = 0$, measurement time interval $\tilde{\tau}_{\rm{m}} = 10 \Delta \tilde{t}$ with $\Delta \tilde{t} = 0.001$, and the fixed parameter $\tilde{\tau}_{\rm{a}} = 1$.