Number of Brain States in an N-Body Dynamical Scenario According to the Universal Bekenstein Entropy Bound

There is an intense interest in the modulation of brain neural circuits and its correlations with different behavioral states, memory, learning, as well as neuropsychological disorders. It is believed that brain cells form functional circuits, process information and mediate behavior. Therefore, the brain system may be thought of as a super-computing machine that turns information into thoughts, memories, and cognitions. Moreover, according to the quantum brain dynamics and quantum conscience hypotheses, quantum theory, the most fundamental theory of matter, may help explain the function of the brain. In the intersection of the architecture of the brain's biological substrate, the processing of information and entropy (as a measure of information processing capacity), and the generation of input to this system (either externally or internally), one may expect to find the foundations of cognition and behavior as an emergent phenomenon. In this chapter, we calculate the entropy Bekenstein bound of the brain, and from that the number of information N in bits that is required to describe the brain down to its tiniest detail. Furthermore, we define the quantity cm_bR_b as brain quantum of action b. Next, we estimate the possible number of states b in the human brain as related to the number of information bits N. Furthermore, we derive an expression for the kinetic energy of a pair of neurons as a function of brain temperature T, the number of information N in bits, and the neuron mass mn as well as the number density of neurons n. We introduce the conjecture that the time rate of r(t) might represent the velocity at which a pair of neurons can approach or recede from each other upon experiencing a transfer of N number of information bits.