Exact Hamiltonian Dynamics of Rare Events in Active Matter
Abstract
Active systems navigate complex environments through non-equilibrium fluctuations, rendering standard equilibrium transition-rate theories inadequate. Moreover, transition rates provide only partial information on how stochastic dynamics explore metastable states, whereas knowledge of the optimal paths offers deeper physical insight. Using an active Ornstein-Uhlenbeck particle, i.e., a particle driven by exponentially correlated noise, as a paradigmatic model, we establish an exact mapping of the non-Markovian optimal path onto a higher-dimensional Hamiltonian dynamical system so that, for arbitrary force fields, optimal paths can be computed systematically by solving the corresponding Hamilton equations. Tuning the conserved energy allows us to explore diverse dynamical regimes, ranging from classical instanton trajectories strictly confined to the zero-energy surface to finite-time optimal paths at non-zero energies, which can spiral around shoulders of the energy landscape, a distinct signature of the non-Markovian active dynamics.
Related
- Active Brownian Dynamics from a Hamiltonian Model: Transitioning from Equilibrium to Activity
- Conservation Laws and Slow Dynamics Determine the Universality Class of Interfaces in Active Matter
- Painlevé Integrability, Hamiltonian Structure and Exact Elliptic Reductions of a Generalized Nonlinear Wave Equation
- The transverse matter Hamiltonian
- Resource-efficient energy-based operator selection in fermionic ADAPT-VQE via exact Hamiltonian transformation
BibTeX
@misc{crisanti2026exact,
title = {{Exact Hamiltonian Dynamics of Rare Events in Active Matter}},
author = {Andrea Crisanti and Matteo Paoluzzi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07496},
eprint = {2609.07496},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07496},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Exact Hamiltonian Dynamics of Rare Events in Active Matter
AU - Andrea Crisanti
AU - Matteo Paoluzzi
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.07496
UR - https://arxiv.org/abs/2609.07496
AB - Active systems navigate complex environments through non-equilibrium fluctuations, rendering standard equilibrium transition-rate theories inadequate. Moreover, transition rates provide only partial information on how stochastic dynamics explore metastable states, whereas knowledge of the optimal paths offers deeper physical insight. Using an active Ornstein-Uhlenbeck particle, i.e., a particle driven by exponentially correlated noise, as a paradigmatic model, we establish an exact mapping of the non-Markovian optimal path onto a higher-dimensional Hamiltonian dynamical system so that, for arbitrary force fields, optimal paths can be computed systematically by solving the corresponding Hamilton equations. Tuning the conserved energy allows us to explore diverse dynamical regimes, ranging from classical instanton trajectories strictly confined to the zero-energy surface to finite-time optimal paths at non-zero energies, which can spiral around shoulders of the energy landscape, a distinct signature of the non-Markovian active dynamics.
ER -