Statistical field theory of the transmission of nerve impulses

Stochastic processes leading voltage-gated ion channel dynamics on the nerve cell membrane are a sufficient condition to describe membrane conductance through statistical mechanics of disordered and complex systems.

Voltage-gated ion channels in the nerve cell membrane are described by the Ising model. Stochastic circuit elements called "Ising Neural Machines" are introduced. Action potentials are described as quasi-particles of a statistical field theory for the Ising system.

The particle description of action potentials is a new point of view and a powerful tool to describe the generation and propagation of nerve impulses, especially when classical electrophysiological models break down. The particle description of action potentials allows us to develop a new generation of devices to study neurodegenerative and demyelinating diseases as Multiple Sclerosis and Alzheimer's disease, even integrated by connectomes. It is also suitable for the study of complex networks, quantum computing, artificial intelligence, machine and deep learning, cryptography, ultra-fast lines for entanglement experiments and many other applications of medical, physical and engineering interest.