representation
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In this paper, we shall focus on a single spin $J$ with spin operators $J_x$, $J_y$, and $J_z$. Instead of working with the density matrix, we approach this problem from a phase-space perspective. The natural phase-space representation for spin systems is through spin coherent states, which are defined as [@Radcliffe1971] $$\label{spin_coherent_states}
|\Omega\rangle= e^{- i \phi J_z} e^{-i \theta J_y} e^{-i \psi J_z} |J,J\rangle,$$ where $|J,J\rangle$ is the angular momentum state with largest quantum number of $J_z$, and $(\theta,\phi,\psi)$ are Euler angles. The angle $\psi$ is not actually necessary and is placed here only for the sake of completeness.

We may define, as a phase-space distribution for this spin system, the Husimi-Q function, $$\label{spin_Q}
\mathcal{Q}(\Omega) = \langle \Omega | \rho | \Omega \rangle.$$ In phase space, the dynamics of Eq. (\[M\]) can be recast into the Fokker-Planck equation for $\mathcal{Q}$, $$\label{FP}
\partial_t \mathcal{Q} = U(\mathcal{Q}) +  \mathcal{D} (\mathcal{Q}),$$ where $U$ accounts for the unitary part of the evolution and $\mathcal{D}$ for the dissipator. The phase-space differential operators $U(\mathcal{Q})$ and $\mathcal{D}(\mathcal{Q})$ may then be obtained from standard operator correspondence tables. The most interesting correspondences are those concerning commutators of the spin operators $J_i$, which translate into the usual orbital angular 