The mechanics underpinning non-deterministic computation in cortical neural networks

Cortical neurons allow random electrical noise to contribute to the likelihood of firing a signal. Previous approaches have involved statistically modeling signaling outcomes in neuronal populations, or modeling the dynamical relationship between membrane potential, ion channel activation, and ion conductance in individual neurons. However, these methods do not mechanistically account for the role of random electrical noise in gating the action potential. Here, the membrane potential of a cortical neuron is modeled as the uncertainty in all component pure states, or the amount of information encoded by that computational unit. With this approach, each neuron computes the probability of transitioning from an off-state to an on-state, with the macrostate of each computational unit being a function of all component microstates. Component pure states are integrated into a physical quantity of information, and the derivative of this high-dimensional probability density yields eigenvalues, or an internally-consistent observable system state at a defined point in time. In accordance with the Hellman-Feynman theorem, the resolution of the system state is paired with a spontaneous shift in charge distribution, and so this defined system state instantly becomes the past as a new probability density emerges. This model of Hamiltonian mechanics produces testable predictions regarding the wavelength of free energy released upon information compression. Overall, this model demonstrates how cortical neurons might achieve non-deterministic signaling outcomes through noisy coincidence detection.