  General characterizations of physical measurements are discussed within the
framework of the classical information theory. The uncertainty relation for
simultaneous measurements of two physical observables is defined in this
framework for generalized dynamic systems governed by a Sturm--Liouville type
of equation of motion. In the first step, the reduction of Kennard--Robertson
type uncertainties due to boundary conditions with a mean-square error is
discussed quantitatively with reference to the information entropy. Several
concrete examples of generalized uncertainty relations are given. Then, by
considering disturbance effects, a universally valid uncertainty relation is
investigated for the generalized equation of motion with a certain boundary
condition. Necessary conditions for violation (reduction) of the
Heisenberg-type uncertainty relation are discussed in detail. The reduction of
the generalized uncertainty relation due to the boundary condition is then
tested experimentally by re-analyzing data for measured electron densities in a
hydrogen molecule encapsulated in a fullerene C60 cage.
