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Electrodynamics Correlates Knock-on and Knock-off: Current is Spatially Uniform in Ion Channels

Ions in channels have been imagined as hard balls in a macroscopic mechanical model, for a very long time. Hard balls interact by collisions in such models, randomly knocking each other on and off `binding' sites in thermal motion. But ions have large charge, and the hard balls of classical models do not. The electrodynamics of charge guarantee strong correlations between the movements of ions on all time scales, even those of atomic scale thermal motion. Correlations are present whenever Maxwell's equations apply, so they are present in individual trajectories, not just averages. Indeed, in a series system like an idealized narrow channel, the correlation is perfect (within the accuracy of Maxwell's equations) because of conservation of total current (that includes Maxwell's displacement current, the ethereal ${\varepsilon }_0{\partial \boldsymbol{\mathrm{E}}}/{\partial t}$).The ethereal component of current prevents spatial variation of total current in a series system. The stochastic complexity of spatial thermal motion disappears for current }in a series system. Total current does not depend on location in a series system like a narrow ion channel on any time scale. Spatial variables are not needed in the description of total current in a one dimensional channel on any time scale, according to the Maxwell equations. Removing the spatial dependence of total current should dramatically simplify theories and simulations, one might imagine.

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