  We derive the semi-classical Lindblad master equation in phase space for both
canonical and non-canonical Poisson brackets using the Wigner-Moyal formalism
and the Moyal star-product. The semi-classical limit for canonical dynamical
variables, i.e., canonical Poisson brackets, is the Fokker-Planck equation, as
derived before. We generalize this limit and show that it holds also for
non-canonical Poisson brackets. Examples are gyro-Poisson brackets, which occur
in spin ensembles, systems of recent interest in atomic physics and quantum
optics. We show that the equations of motion for the collective spin variables
are given by the Bloch equations of nuclear magnetization with relaxation. The
Bloch and relaxation vectors are expressed in terms of the microscopic
operators: The Hamiltonian and the Lindblad functions in the Wigner-Moyal
formalism.
