Deterministic active particles in the overactive limit

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 nearly 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 even if the confining potential is time-independent.