A universal resolution limit: '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

Franz-Josef Schmitt

nov 2010 · GRIN Verlag

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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 DO is the same like a variance of the probability D

for measuring O : DO = D

* O . Implications of these findings are shortly discussed.