Notes on The Energy Equivalence of Information

Maxwell's demon makes observations and thereby collects information. As Brillouin points out such information is the negative of entropy (negentropy) and is the equivalent of a cost in energy. The energy cost of information can be quantified in the relationship E = kT ln 2, where k is the Boltzmann constant, T is the absolute temperature, and the factor ln 2 arises from the existence of two possibilities for a "yes/no" circumstance, as, for example, in the passage of a proton through a barrier controlled by a Maxwell's demon. This paper considers further conclusions that follow from the quantification of the energy cost of information. First, consideration of the minimum uncertainty in the measurement of energy cost of information leads to an expression for the uncertainty in the corresponding time of the measurement, which depends inversely upon temperature at which the measurements occur. Second, because of the universal connection between energy and mass, an almost imperceptible mass accompanies the accumulation of information. And third, to account for the total free energy change that describes the action of adenosine triphosphate (ATP) synthase, an additional term is suggested to be appended to the Mitchell chemiosmotic equation, which describes this process. The additional term accounts for the energy cost of sorting away from background ions those protons allowed to enter the ATP synthase.