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

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.

💡 Research Summary

In this work the authors introduce a novel active particle, the Ornstein‑Uhlenbeck information particle (OUIP), which derives its propulsion from an information engine rather than a constant external force. Starting from the classic under‑damped Brownian particle, they add either a fixed self‑propulsion term γₜU₀ (the usual self‑propelled particle, SPP) or a feedback‑controlled Ornstein‑Uhlenbeck (OU) noise term u(t). The OU noise is switched between two persistence‑time regimes, β₁ and β₂, depending on whether the instantaneous parallel velocity v∥ is below or above a preset threshold v₀. This switching implements a Szilard‑type information‑to‑work conversion: the particle’s velocity is measured at intervals τₘ, and the measured outcome determines which OU dynamics will be applied until the next measurement.

The equations of motion are rendered dimensionless using the inertial delay time τ=m/γₜ, the thermal velocity v_T=√(k_BT/m) and a characteristic length l₀=√(mk_BT)/γₜ. The key control parameters become the reduced mass ˜M=m k_BT/(γₜγᵣ), the OU perturbation strength ˜A=Aγₜ/(k_BT), the persistence time ˜τₐ=τₐ/τ, and the measurement interval ˜τₘ=τₘ/τ. Numerical simulations are performed in a periodic square box; after an equilibration of 10³τ the authors collect data for 5.5×10⁵τ.

Both SPP and OUIP acquire a finite average velocity ⟨ṽ∥⟩ along their orientation, but their velocity distributions differ dramatically. The SPP shows a single asymmetric peak near the imposed speed U₀ and a Gaussian low‑speed tail caused by inertia. In contrast, the OUIP exhibits a bimodal distribution: one Gaussian centered at zero (slow diffusion mode) and another near the threshold v₀ (fast traveling mode). The corresponding Cartesian component ṽₓ displays a stretched‑exponential tail with exponent α≈1, reflecting the OU‑bath modulation. The two modes are clearly separated in P(ṽ∥) and P(ṽₓ), and the transition between them is discontinuous at |ṽₓ|≈v₀.

A central finding is that the relative weight of the two modes can be tuned by the reduced mass ˜M. Larger inertia (higher ˜M) enhances the low‑speed diffusion mode, while stronger viscous damping (smaller ˜M) favors the high‑speed traveling mode. This demonstrates that the competition between inertial delay and environmental dissipation governs the particle’s dynamical state.

When the threshold is set to zero (v₀=0), the average speed ⟨ṽ∥⟩ becomes a monotonic function of the OU‑noise strength ˜A. For small ˜A the dependence is linear, ⟨ṽ∥⟩∝˜A, whereas for large ˜A it follows a square‑root law, ⟨ṽ∥⟩∝˜A^{1/2}. This behavior can be interpreted as an effective temperature T*≈T