Abstract
We conducted an investigation into the impact of an external magnetic field on graphene under two proposed conditions: a constant magnetic field (ω), and a field characterized by exponential decay (μ). The resulting eigenvalue solutions were utilized to analyze the Shannon entropy of low-lying states and thermodynamic properties. Regarding Shannon entropy, we observed that both conditions led to increased fermion localization in position space and delocalization in momentum space. Furthermore, we calculated the BBM entropic uncertainty relation and confirmed its validity in one dimension. As for the thermodynamic properties, we found that augmenting the influence of the magnetic fields altered their respective behaviors.
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