Definition of dB Absolute. Energy Efficiency Metric It is already well known that the Xxxxxxx channel capacity theorem can be simply manipulated to offer the theoretical minimum heat dissipation required to transmit a bit of information. We start from the formula [64]: where C is the channel capacity (in b/s), B is the channel bandwidth (Hz), S is the signal power, and N is the noise power. By considering purely thermal noise as the fundamental noise source in a transmission system, we have the N=kTB, where k is the Boltzmann constant, T is the absolute temperature (in kelvins), and B is again the system bandwidth. In the limit of allowing B to increase to infinity, the noise power also tends towards infinity, and we can take advantage of the approximation as . We note that attempting to exploit the maximal (infinite) system spectrum (the full bandwidth as ) is analogous to an OFDM or DMT- based communications system, where all bandwidth slots are each maximally exploited with respect to how much data can be transmitted along each frequency slot. In the case as , a slot may offer an exceedingly low data bandwidth; however, we can still exploit whatever minimal data capacity may be available. In the limit as , the Xxxxxxx channel capacity equation tends to: Rearranging the equation (1b), we find that . The quantity S/C is the quotient of the signal power with the channel capacity, and is equivalent to the number of joules per bit (J/b) of information transmitted across the channel, and is equal to kTln2. In other words, as we have already argued from alternative fundamental considerations [58][59], the quantity kTln2 represents the minimum amount of energy dissipated by the transfer of information; in addition in ref. [65] we also argue that this energy is essentially irreversibly lost (i.e. it is associated with an increase in entropy of kln2 per bit of data.) We have used this minimum energy dissipation per bit to define a decibel-based, absolute energy efficiency metric, dB, which offers an objective means to establish the energy efficiency of any information processing system [61]. This is defined as follows: dB = 10 log æ ö e 10 çè kT ln 2 ÷ø
