an ideal choice, as it is also related to the Rényi-2 entropy. However, the question of how this formalism could be extended to other systems was not explored.

The goal of this work is to derive a theory of entropy production that is applicable to spin systems subject to general reservoirs. To achieve this goal, we shall follow a similar approach as in [@Santos2017b] and use phase-space techniques based on spin coherent states and the spin Husimi-Q function [@1940264]. The Husimi function is a quasiprobability distribution commonly used to study the correspondence between quantum and classical dynamics [@PhysRevLett.55.645]. Among its properties, it is always positive definite. This fact was used by Wehrl [@Wehrl1978; @Wehrl1979; @lieb1978; @Araki1970] to define a phase-space version of the Shannon entropy. The Wehrl entropy is not a measure of the purity of the wave function as is the von Neumann entropy, but is directly related to the uncertainty area of the Husimi function in phase space [@General1995; @Buek1995; @PhysRevA.54.729]. For any state, the Wehrl entropy provides an upper bound to the von Neumann entropy, which is saturated only for the case of a coherent state [@lieb1978; @lieb2014]. The paper is organized as follows. In Sec. \[sec:spin\_ps\_dynamics\], 