Canonical active Brownian motion and bifurcation phenomena

Active Brownian particles possess depots of internal energy which they can convert into mechanical energy, leading to complex patterns of stochastic motion. Applications of this concept range from the modelling of the behaviour of biological systems to extensions of the stochastic quantization scheme in quantum field theory. Theories of active Brownian motion so far imposed couplings between the internal energy and the kinetic energy of the system. We investigate how this idea can be naturally taken further to include also couplings to the potential energy, which finally leads to a general theory of canonical dissipative systems. Apart from stationary solutions, we study non-equilibrium dynamics and show the existence of various bifurcation phenomena. (author)