we present the framework for describing spin systems in phase space. We do so using two equivalent approaches, one based on spin coherent states and the other based on the Schwinger mapping to bosonic systems. We thus obtain two definitions for the Husimi function and for the corresponding Wehrl entropy. In Sec. \[sec:dephasing\_channel\], we study the Wehrl entropy production for the dephasing channel and also discuss, as an application, the dynamics of a spin $1/2$ in a rotating magnetic field. In Sec. \[sec:amplitude\_damping\], we apply our formalism to the finite-temperature amplitude damping channel and give general expressions for the Wehrl entropy production rate and entropy flux rate, which are valid for any temperature and spin number. We also show the relation between the Wehrl entropy flux rate and the energy flux rate. Explicit results for the spin-$1/2$ case are given as well. In Sec. \[sec:applications\], we apply these results to the problems of spontaneous emission, thermal quenches, and a spin $1/2$ in an oscillating magnetic field. Finally, in Sec. \[sec:fred\], we study the entropy production of a two-level system interacting with a single-photon pulse. The conclusions are summarized in Sec. \[sec:conclusions\].

\[sec:spin\_ps\_dynamics\] Spin phase space dynamics
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Spin coherent state 