The Onsager reciprocal relations express the equality of certain ratios between flows and forces in thermodynamical systems out of equilibrium, but where a notion of local equilibrium exists. This is exactly the case for a neuron during producing an action potential. The closest relative to our derivation is the Poisson-Nernst-Planck (PNP) and its mathematically simplified version (Poisson-Boltzmann-Nernst-Planck) [114] model are based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. Given that the Nernst-Planck equation is essentially a flux equation for the special case of zero flux, furthermore that Planck essentially included Fick’s second law in the PNP model, our approach seems to be self-consistent and a significant extension to the famous model. As we discussed, it is not reasonable to calculate a mean value for those vastly different interaction speeds. We derived a realistic approach to the ion transport problems, in many areas; in addition to biological systems, also for semiconductor devices and nanofluidic systems.
Biological cells comprise components such as electrolytes, semipermeable membranes, solutions with expremely different concentration. Surprisingly, they show spontaneous electrical activity. As Eq.(2.24) shows, the electrical interaction speed is million times higher than the chemical one.