Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2006-10-24
AIP Conf. Proc. 872, 55 (2006)
Physics
Condensed Matter
Statistical Mechanics
8 pages, 2 eps figures, presented at the 26-th International Workshop on Bayesian Inference and Maximum Entropy Methods in Sci
Scientific paper
10.1063/1.2423260
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.
Bakar Burhan
Lemmens L. F.
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