Scalar field theory for (chiral) active Brownian particles: bottom-up derivation revisited
Abstract
The active Brownian particle (ABP) model is one of the most widely used particle-based models in studies of scalar active fluids. A collection of interacting ABPs is known to exhibit intriguing phenomena that are absent in equilibrium counterparts. A prominent example is spontaneous phase separation, known as motility-induced phase separation (MIPS), which occurs even in the absence of explicit attractive interactions. In parallel, the large-scale behavior of scalar active fluids is often modeled using continuum descriptions, namely, scalar field theories. Such scalar active field theories are usually formulated in a top-down manner, and establishing their connections to particle-based models remains challenging, with these connections not yet fully understood. To advance the microscopic derivation of scalar active field theories, we revisit the connection between ABPs interacting via a two-body potential in two dimensions and scalar field theories that include all possible terms up to fourth order in spatial gradients. Our approach is based on a pressure expansion and the renormalization group (RG) method in the context of singular perturbation theory. The RG method provides a systematic way to eliminate fast variables and identify the dynamics on the slow invariant manifold. Within this framework, scalar field theories can be obtained as RG flow equations. We also apply this method to a chiral variant of the ABP model, the chiral ABP (cABP) model, in which a constant torque biases particle rotation to the left or right. We show that the scalar field theory corresponding to the cABP model contains two ``odd'' terms in addition to those present in the scalar field theory for ABPs. The method developed here may also be useful for deriving hydrodynamic descriptions of other types of active matter systems.
Related
- Parity-violating scalar-tensor theory revisited: complete basis up to d=4 and Hamiltonian analysis
- Stationary distribution of active Brownian particles in a bounded domain
- Diffusion of chiral active Brownian particles in oscillatory Poiseuille flow
- Static and dynamic density correlations of interacting active Brownian particles
- Collective adaptation to time-dependent targets for active Brownian particles
BibTeX
@misc{kuroda2026scalar,
title = {{Scalar field theory for (chiral) active Brownian particles: bottom-up derivation revisited}},
author = {Yuta Kuroda and Thomas Speck},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01672},
eprint = {2610.01672},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01672},
}
RIS
TY - UNPB
TI - Scalar field theory for (chiral) active Brownian particles: bottom-up derivation revisited
AU - Yuta Kuroda
AU - Thomas Speck
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01672
UR - https://arxiv.org/abs/2610.01672
AB - The active Brownian particle (ABP) model is one of the most widely used particle-based models in studies of scalar active fluids. A collection of interacting ABPs is known to exhibit intriguing phenomena that are absent in equilibrium counterparts. A prominent example is spontaneous phase separation, known as motility-induced phase separation (MIPS), which occurs even in the absence of explicit attractive interactions. In parallel, the large-scale behavior of scalar active fluids is often modeled using continuum descriptions, namely, scalar field theories. Such scalar active field theories are usually formulated in a top-down manner, and establishing their connections to particle-based models remains challenging, with these connections not yet fully understood. To advance the microscopic derivation of scalar active field theories, we revisit the connection between ABPs interacting via a two-body potential in two dimensions and scalar field theories that include all possible terms up to fourth order in spatial gradients. Our approach is based on a pressure expansion and the renormalization group (RG) method in the context of singular perturbation theory. The RG method provides a systematic way to eliminate fast variables and identify the dynamics on the slow invariant manifold. Within this framework, scalar field theories can be obtained as RG flow equations. We also apply this method to a chiral variant of the ABP model, the chiral ABP (cABP) model, in which a constant torque biases particle rotation to the left or right. We show that the scalar field theory corresponding to the cABP model contains two ``odd'' terms in addition to those present in the scalar field theory for ABPs. The method developed here may also be useful for deriving hydrodynamic descriptions of other types of active matter systems.
ER -