For compact metric graphs with Dirichlet conditions, the heat content is shown to equal the volume minus a boundary term plus a weighted sum over Dirichlet-to-Dirichlet paths, for all positive times.
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On the heat content of compact quantum graphs
For compact metric graphs with Dirichlet conditions, the heat content is shown to equal the volume minus a boundary term plus a weighted sum over Dirichlet-to-Dirichlet paths, for all positive times.