  A typical linear open system is often defined as a component of a larger
conservative one. For instance, a dielectric medium, defined by its frequency
dependent electric permittivity and magnetic permeability is a part of a
conservative system which includes the matter with all its atomic complexity. A
finite slab of a lattice array of coupled oscillators modelling a solid is
another example. Assuming that such an open system is all one wants to observe,
we ask how big a part of the original conservative system (possibly very
complex) is relevant to the observations, or, in other words, how big a part of
it is coupled to the open system? We study here the structure of the system
coupling and its coupled and decoupled components, showing, in particular, that
it is only the system's unique minimal extension that is relevant to its
dynamics, and this extension often is tiny part of the original conservative
system. We also give a scenario explaining why certain degrees of freedom of a
solid do not contribute to its specific heat.
