Deterministic active particles in the overactive limit

TL;DR

This paper analyzes deterministic active particles in a fixed-speed limit, revealing Hamiltonian dynamics for identical particles and phase volume contraction for non-identical ones, depending on potential time-dependence.

Contribution

It introduces a Hamiltonian formulation for deterministic active particles at fixed speed and explores phase volume behavior based on particle identity and potential time-dependence.

Findings

Hamiltonian system formulation for fixed-speed particles in static potentials

Conservation of phase volume for identical particles

Phase volume shrinks for non-identical particles in static potentials

Abstract

We consider two models of deterministic active particles in an external potential. In the limit where the speed of a particle is fixed, both models coincide and can be formulated as a Hamiltonian system, but only if the potential is time-independent. If the particles are identical, their interaction via a potential force leads to conservative dynamics with a conserved phase volume. In contrast, the phase volume is shown to shrink for non-identical particles.