Franz-Josef Schmitt 
A universal resolution limit [EPUB ebook] 
‘The lower bound on the energy for bounded systems is equivalent to the Bekenstein upper bound on the entropy to energy ration for bounded systems

Scientific Essay from the year 2009 in the subject Physics – Theoretical Physics, Technical University of Berlin, language: English, abstract: Several approaches can be used to proof the
assumption that an universal upper bound on the entropy to
energy ratio (S/E) exists in bounded systems. In 1981 Jacob
D. Bekenstein published his findings that S/E is limited by
the “effective radius” of the system and mentioned various
approaches to derive S/E employing quantum statistics or
thermodynamics.
It can be shown that similar results are obtained considering
the energetic difference of longitudinal eigenmodes inside a
closed cavity like it was done by Max Planck in 1900 to
derive the correct formula for the spectral distribution of the
black-body radiation. Considering an information
theoretical approach this derivation suggests that the
variance of an expectation value D is the same like a
variance of the probability D

for measuring O :
D = D

* . Implications of these findings are shortly
discussed.