Hamiltonian model for the Brownian motion of a rigid rotor

We derive stochastic equations for the motion of a rigid rotor in a linear heat bath starting from a fully dynamical (Hamiltonian) description. We obtain a generalized Langevin equation for the angular velocity of the rotor in which the fluctuations in the torque arise from the initial conditions of the heat bath. The dissipation is in general nonlinear and is related to the fluctuations via a fluctuation-dissipation relation that is a natural consequence of our description.