Probability assignment in a quantum statistical model

TL;DR

This paper compares two different probability assignment methods in a quantum statistical model of nano-magnets, showing that the Markov process-based approach makes fewer assumptions and aligns better with thermodynamic principles.

Contribution

It introduces a novel probability assignment based on a Markov process mapping and demonstrates its advantages over the traditional von Neumann entropy-based approach.

Findings

The two probability assignments produce numerically different PDFs for the same observable.

The Markov process-based assignment makes fewer assumptions according to the maximum entropy principle.

The Markov-based assignment is compatible with the Gibbs procedure in thermal equilibrium.

Abstract

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.