of integration [@jlgh] does not involve any stochastic process whatsoever.

Classical Spin Baths {#sec:csb}
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[ Contrary to what some books in quantum mechanics state (in the authors’s knowledge, an exception is Schulman’s book [@schulman]), the concept of spin can be defined in an entirely classical way . In practice, spinors provide a more fundamental representation of the rotation group than that given by tensors [@schulman; @cartan; @hladik; @carmeli; @barut]. Hence, one can think of a collection, [e.g.]{}, a bath, of DOF comprising classical spinors (or, for brevity, spins): a classical spin-bath. An example of a classical spin baths is given by the Classical Heisenberg Model [@huang], whose Hamiltonian is $$H_{CHS}=\sum_{a=x,y,z}\sum_{I,J}^N S_a^I {\cal C}_{IJ}^a S_a^J \;,$$ where ${\bf S}^I$ are $N$ classical vectors obeying the constraint $$\left(S_x^I\right)^2 + \left(S_y^I\right)^2 + \left(S_z^I\right)^2 =1 \;,$$ for $I=1,...,N$, and the ${\cal C}_{IJ}^a$ are coupling constants. ]{} [However, since the generalization to baths with many spins is straightforward, in the following, we will illustrate the theory using a bath comprising a single classical spin]{}. Consider a classical spin vector $\bf S$, with components $S_a$, $a=x,y,z$, and Hamiltonian $H^{\rm S}({\bf S})$. Let us define the spin gradient as $\nabla^{\bf S}=\partial/\partial{\bf S}$, which in terms of 