Dissipative contributions of internal multiplicative noise

We analyze the relaxation of a spin interacting with a heat bath of other spins, in an external magnetic field, starting from a fully dynamical (Hamiltonian) description. We derive a generalized Langevin equation for the spin system in which the initial conditions of the bath spins act as fluctuations. The generalized Langevin equation has multiplicative fluctuations and nonlinear dissipation (relaxation) contributions which obey a fluctuation-dissipation theorem. As a natural consequence, our spin system relaxes to a canonical distribution.