  In this paper we prove that a large class of linear evolution PDEs defines a
Stokes-Dirac structure over Hilbert spaces. To do so, the theory of boundary
control system is employed. This definition encompasses problems from
mechanics, that cannot be handled by the seminal geometric setting given in
[van der Schaft and Maschke, Hamiltonian formulation of distributed-parameter
systems with boundary energy flow, 2002 ]. Many worked-out examples stemming
from continuum mechanics and physics are presented in detail, and a particular
focus is given on the functional spaces in duality at the boundary of the
geometrical domain. For each example, the connection between the differential
operators and the associated Hilbert complexes is illustrated.
