Hamiltonian active particles in an environment

We examine a Hamiltonian system which represents an active particle that can move against an opposing external force by drawing energy from an internal depot while immersed in a noisy and dissipative environment. The Hamiltonian consists of two subsystems, one representing the active particle's motion and the other its depot of "fuel." We show that although the active particle loses some of its energy to dissipation from the environment, dissipation can also help to stabilize the dynamical process that makes the particle active. This raises the possibility that the internal mechanisms of active particles may not only be able to operate in noisy and dissipative environments, but may actually rely on the environment for their control.