  We introduce the stochastic Boltzmann equation (SBE) as an approach for
exploring the spin dynamics of magnetic molecules coupled to a stochastic
environment. The SBE is a time-evolution equation for the probability density
of the spin density matrix of the system. This probability density is relevant
to experiments which take measurements on single molecules, in which
probabilities of observing particular spin states (rather than ensemble
averages) are of interest. By analogy with standard treatments of the regular
Boltzmann equation, we propose a relaxation-time approximation for the SBE, and
show that solutions to the SBE under the relaxation-time approximation can be
obtained by performing simple trajectory simulations for the case of a boson
gas environment. Cases where the relaxation-time approximation are satisfied
can therefore be investigated by careful choice of the parameters for the boson
gas environment, even if the actual environment is quite different from a boson
gas. The application of the SBE approach is demonstrated through an
illustrative example.
