# 6G Cognitive Information Theory: A Mailbox Perspective
## 9 Energy Consumption Optimization in Cognitive Information
### Energy Efficient Cognitive Information  
The optimization problems in cognitive information have been widely studied. In traditional analysis, [PERSON]'s formula defines the theoretical limit of information transmission, and [PERSON]'s principle defines the lower limit of energy consumption for information processing. However, there have been no theories to explain the measurement of value. Specifically, the process of information transmission follows [PERSON]'s signaling capacity theory and, by measuring the changes in the information entropy in the process of information transmission, [PERSON] expresses the transmission capacity of a random signaling channel with a formula. In contrast, [PERSON]'s principle indicates that the micro computation of information in computing chips will generate heat, i.e., it will change the thermodynamic entropy of computing chips and the nearby region, there will be a lower limit of computation energy consumption, and the computation of a piece of information will be accompanied with specific minimum energy consumption. Thus, according to the principle of thermodynamic entropy, the entropy increase of computing chips and the nearby region results from the process of computing. This can be realized through heat transfer, and thus the computing energy consumption can be presented in the form of heat energy. However, the aforementioned computation does not consider the value of information. First, the energy consumed by transmission is calculated. According to [PERSON]'s formula, the maximum transmission rate of information \(C_{tran}\) can be obtained as follows:  
\[C_{tran}=W\log_{2}^{1+\frac{C_{tran}t}{W\log_{2}^{1}}}, \tag{1}\]where \(W\) denotes the transmission bandwidth, \(p_{tran}\) is the transmission power, \(N_{0}\) represents the noise, and \(h\) is the transmission distance. Therefore, the transmission power is expressed as:  
\[p_{tran}=\frac{(2^{\frac{C_{temp}}{W}}WN_{0})}{h}. \tag{2}\]  
The energy consumption denotes the energy consumed when handling computing information, and it mainly includes the energy consumed by the information processor. According to [PERSON]'s principle, the minimum energy required to wipe off 1 bit of information is obtained as:  
\[E_{comp}=kT\ln(2), \tag{3}\]  
where \(k\) denotes the Boltzmann constant, and \(k=1.38\times 10^{-23}J/K\); \(T\) is the temperature in Kelvin degrees; thus, there is a lower limit in the processing of information. In addition, there is a certain space for optimization in the development of chip technology. Besides, there is a gap between the existing power consumption and [PERSON]'s limit. Next, is the calculation of the computation energy consumption. It can be divided into energy consumed for information processing (including the processing of information value) and energy consumed by information communication. Therefore, the total computation amount for both processing and communication of information can be expressed as:  
\[C_{comp}=\sigma_{1}C_{tran}+\sigma_{2}C_{tran}, \tag{4}\]  
where \(\sigma_{1}\) is the logical operand corresponding to each bit of information in communication, and \(\sigma_{2}\) is the logical operand corresponding to each bit of information in the processing algorithm of computation. Thus, the computation energy consumption can be expressed as:  
\[p_{comp}=C_{comp}F\alpha G_{s}k\ln 2, \tag{5}\]  
where \(F\) is the fan-out coefficient of the gate circuit, and \(\alpha\) is the activator. Based on the above discussions, in the process of wireless communication, the communication energy consumption when the channel capacity is reached can be measured using the Shannon channel capacity formula. In the process of information computation, the computation energy consumed in the process of information processing can be measured using Landauer's limits and transistor process technology.