arXiv:2603.25211v3 Announce Type: replace Abstract: This paper presents a port-Hamiltonian formulation of backlash-driven hysteretic energy storage elements. First, we revisit the passivity property of backlash-driven storage elements by presenting a family of storage functions. We explicitly derive the corresponding available storage and required supply functions in the sense of Willems, and show the interlacing property of the aforementioned family of storage functions sandwiched between the available storage and required supply functions. Second, using the obtained family of storage functions, we present a port-Hamiltonian formulation of hysteretic inductors. In particular, we show how an appropriate Hamiltonian function is defined using the family of storage functions and how the hysteretic elements can be expressed as a port-Hamiltonian system with feedthrough term, where the feedthrough term represents energy dissipation. Correspondingly, we illustrate its applicability in describing an RC circuit (in parallel and in series) containing a backlash inductor.