  This thesis discusses the possibility of uncertainty relations for space and
energy given a state of fixed entropy. In particular, it discusses the results
in the paper of Dam/Nguyen. There, the authors propose a lower bound for the
mixed cost in energy and space required for physically storing information in a
quantum mechanical system. We first critically examine the justifications for
the bound given in the paper.This is done from a mathematical point of view, in
contrast to the more physically motivated original paper.Then we give two
examples that illustrate the limitations of this inequality. We also present
numerical results to find an alternative energy-space bound in the finite
dimensional version of this problem. They indicate a slightly different version
of the inequality. In the end we describe a promising ansatz to find a lower
energy-space bound that depends on the amount stored information. Unfortunately
that did not result in a satisfactory result.
