Active Motion in Systems with Energy Supply

Biological motion, human traffic and many other types of active motion rely on the supply of energy. In order to derive a rather general approach for active motion, we have proposed a model of active Brownian particles, which have the ability to take up energy from their environment, to store it in an internal energy depot and to convert internal energy to perform different activities, such as metabolism, acceleration of motion, changes of the environment, or signal-response behavior. The basic description is given by an extended Langevin equation for the motion of the particles, which is coupled to a balance equation for the internal energy depot. Different to the case of passive Brownian motion, we find several new features of the dynamics, such as non-equilibrium velocity distributions, uphill motion, transitions between Brownian and directed motion, or excited collective motion and spontaneous rotations in an ensemble of active particles.