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This thesis discusses the possibility of uncertainty relations for space andenergy given a state of fixed entropy. In particular, it discusses the resultsin the paper of Dam/Nguyen. There, the authors propose a lower bound for themixed cost in energy and space required for physically storing information in aquantum mechanical system. We first critically examine the justifications forthe bound given in the paper.This is done from a mathematical point of view, incontrast to the more physically motivated original paper.Then we give twoexamples that illustrate the limitations of this inequality. We also presentnumerical results to find an alternative energy-space bound in the finitedimensional version of this problem. They indicate a slightly different versionof the inequality. In the end we describe a promising ansatz to find a lowerenergy-space bound that depends on the amount stored information. Unfortunatelythat did not result in a satisfactory result.

A Quantum Mechanical Bound for Space-Energy Cost with Respect to the Von Neumann Entropy