I am doing a research on active matter and I see there are two main ways to introduce the activity to a particle (or set of particles). The most straightforward is introducing an intrinsic velocity in the Brownian dynamics of the particles, also considering a rotational diffusion of this velocity vector. This is known as the Active Brownian Particle (ABP) model. Another way is to apply a coloured noise through an Ornstein-Uhlenbeck process, which gives an exponentially correlated noise, or "active noise".
What is not clear to me is the fact that when you introduce this active noise, what is actually being done is to simulate the interaction with an "active bath", therefore the particles themselves are passive colloids in an active bath. I get how that works, but is there any physical difference in behavior between an ABP and a passive colloid in contact with an active bath? Or are both different approaches for the same physical system?
Any thoughts or references are welcome.
