  The evolution of a quantum system, appropriate to describe nano-magnets, can
be mapped on a Markov process, continuous in $\beta$. The mapping implies a
probability assignment that can be used to study the probability density (PDF)
of the magnetization. This procedure is not the common way to assign
probabilities, usually an assignment that is compatible with the von Neumann
entropy is made. Making these two assignments for the same system and comparing
both PDFs, we see that they differ numerically. In other words the assignments
lead to different PDFs for the same observable within the same model for the
dynamics of the system. Using the maximum entropy principle we show that the
assignment resulting from the mapping on the Markov process makes less
assumptions than the other one. Using a stochastic queue model that can be
mapped on a quantum statistical model, we control both assignments on
compatibility with the Gibbs procedure for systems in thermal equilibrium and
argue that the assignment resulting from the mapping on the Markov process
satisfies the compatibility requirements.
