In this paper, we would like to measure how the magnetic effect appears in the heat trace formula associated with the magnetic Laplacian and the magnetic Dirichlet-to-Neumann operator. We propose to the reader an overview of magnetic heat trace formulas through explicit examples. On the way we obtain new formulas and in particular we calculate explicitly some nonlocal terms and logarithmic terms appearing in the Steklov heat trace asymptotics.
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