Successive patterns of activation and deactivation in local areas of the brain indicate the mechanisms of information processing in the brain. It is possible that this process can be optimized by principles, such as the maximization of mutual information and the minimization of energy consumption. In the present paper, I showed evidence for this argument by demonstrating the correlation among mutual information, the energy of the activation, and the activation patterns. Modeling the information processing based on the functional connectome datasets of the human brain, I simulated information transfer in this network structure. Evaluating the statistical quantities of the different network states, I clarified the correlation between them. First, I showed that mutual information and network energy have a close relationship, and that the values are maximized and minimized around a same network state. This implies that there is an optimal network state in the brain that is organized according to the principles regarding mutual information and energy. On the other hand, the evaluation of the network structure revealed that the characteristic network structure known as the criticality also emerges around this state. These results imply that the characteristic features of the functional network are also affected strongly by these principles. To assess the functional aspects of this state, I investigated the output activation patterns in response to random input stimuli. Measuring the redundancy of the responses in terms of the number of overlapping activation patterns, the results indicate that there is a negative correlation between mutual information and the redundancy in the patterns, suggesting that there is a trade-off between communication efficiency and robustness due to redundancy, and the principles of mutual information and network energy are important to network formation and its function in the human brain.

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