On Energy Expenditure per Unit of the Amount of Information

It is shown that for an equilibrium state of time-symmetric system of non-relativistic strings the energy per unit of information transfer (storage, processing) obeys the Bekenstein conjecture. The result is based on a theorem due to A.Kholevo relating the physical entropy and the amount of information. Interestingly, the energy in question is the difference between the ensemble averaged energy and the Helmholtz free energy. The problem about the energy requirements for the storage, transfer , and processing of information is one of the most important problems in the physics of information. In view of the recent keen interest ( and the attendant very large body of research work) in possible realizations of quantum computers, the above problem has direct relevance to quantum systems. Therefore it seems appropriate to revisit this problem. At the beginning of 1990’s B.Schumacher proposed (and later elaborated) [1] a conjecture (a generalization of earlier proposals by Bekenstein [2] and Pendry [3]) about an existence of a quantum limit for the power requirements of a communication channel. The conjecture relates an amount of information H conveyed by a quantum channel in a time interval δt and the energy E required for the physical representation of the information in the quantum