On the nonlinear dynamics of quantum fluctuations

We formulate stochastic equations for irreversible processes of quantum-mechanical macrovariables in systems which are initially in states near or arbitrarily far from thermal equilibrium, respectively. The derivation is formulated in the Heisenberg picture similar to the well-established derivation of Fokker-Planck equations for classical variables, however, an inner product is introduced that allows to observe the noncommutability of quantum variables.