Barcode entropy for Reeb flows on contact manifolds with Liouville fillings

We study the topological entropy of Reeb flows on contact manifolds with Liouville fillings. With the theory of persistence modules, we define SH-barcode entropy from the symplectic homology of a filling. We prove that the SH-barcode entropy is independent of the choice of the filling and that the barcode entropy provides a lower bound for the topological entropy of the Reeb flow.