The subject under study is an open subsystem of a larger linear and
conservative system and the way in which it is coupled to the rest of system.
Examples are a model of crystalline solid as a lattice of coupled oscillators
with a finite piece constituting the subsystem, and an open system such as the
Helmholtz resonator as a subsystem of a larger conservative oscillatory system.
Taking the view of an observer accessing only the open subsystem we ask, in
particular, what information about the entire system can be reconstructed
having such limited access. Based on the unique minimal conservative extension
of an open subsystem, we construct a canonical decomposition of the
conservative system describing, in particular, its parts coupled to and
completely decoupled from the open subsystem. The coupled one together with the
open system constitute the unique minimal conservative extension. Combining
this with an analysis of the spectral multiplicity, we show, for the lattice
model in particular, that only a very small part of all possible oscillatory
motion of the entire crystal, described canonically by the minimal extension,
is coupled to the finite subsystem.