Active Brownian Dynamics from a Hamiltonian Model: Transitioning from Equilibrium to Activity
Abstract
We introduce a Hamiltonian Active Brownian Particle (HABP) model that connects equilibrium dynamics with the non-equilibrium, two-dimensional overdamped behavior of standard Active Brownian Particles (ABPs). In equilibrium, the system follows overdamped Langevin equations that strictly satisfy the fluctuation-dissipation theorem. Coupling translational and rotational degrees of freedom to separate heat baths (Tθ > Ttr), drives the system out of equilibrium. In free space, matching the diffusion coefficients yields quantitative agreement with the ABP model in the limit Tθ/Ttr→ ∞, whereas in a harmonic potential, this matching is recovered even at finite temperature ratios. Entropy production analysis demonstrates that in the ABP limit, all energy injected by the swim force dissipates into the translational bath, leaving the rotational bath as a zero-cost entropy source. These insights provide the first steps toward equilibrium-inspired descriptions of active matter, facilitating the development of new theoretical frameworks to study activity-induced fluctuations, transport, and phase behavior in living and non-living soft matter systems far from equilibrium.
Related
- Temperature--Hamiltonian Ambiguity in Strong-Coupling Quantum Equilibrium
- Neural Non-Equilibrium Hamiltonian Monte Carlo for Corrected Boltzmann Sampling
- A Brownian dynamics study of liquid–liquid phase separation in multiscale chromatin networks
- Broadband molecular dynamics simulation of confined Brownian motion
- A Hybrid Brownian Dynamics-kinetic Monte Carlo Framework for Coupled Magnetic and Rotational Dynamics of Nanoparticles
BibTeX
@misc{bhattacharya2026active,
title = {{Active Brownian Dynamics from a Hamiltonian Model: Transitioning from Equilibrium to Activity}},
author = {Antik Bhattacharya and Smarajit Karmakar and Jürgen Horbach},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30670},
eprint = {2608.30670},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30670},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Active Brownian Dynamics from a Hamiltonian Model: Transitioning from Equilibrium to Activity
AU - Antik Bhattacharya
AU - Smarajit Karmakar
AU - Jürgen Horbach
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.30670
UR - https://arxiv.org/abs/2608.30670
AB - We introduce a Hamiltonian Active Brownian Particle (HABP) model that connects equilibrium dynamics with the non-equilibrium, two-dimensional overdamped behavior of standard Active Brownian Particles (ABPs). In equilibrium, the system follows overdamped Langevin equations that strictly satisfy the fluctuation-dissipation theorem. Coupling translational and rotational degrees of freedom to separate heat baths (T_θ > T_tr), drives the system out of equilibrium. In free space, matching the diffusion coefficients yields quantitative agreement with the ABP model in the limit T_θ/T_tr→ ∞, whereas in a harmonic potential, this matching is recovered even at finite temperature ratios. Entropy production analysis demonstrates that in the ABP limit, all energy injected by the swim force dissipates into the translational bath, leaving the rotational bath as a zero-cost entropy source. These insights provide the first steps toward equilibrium-inspired descriptions of active matter, facilitating the development of new theoretical frameworks to study activity-induced fluctuations, transport, and phase behavior in living and non-living soft matter systems far from equilibrium.
ER -