Large deviations of ionic currents in dilute electrolytes

TL;DR

This paper uses macroscopic fluctuation theory to analyze rare ionic current fluctuations in dilute electrolytes, revealing Gaussian behavior at small voltages and non-Gaussian distributions at large voltages, constrained by thermodynamic principles.

Contribution

It derives the optimal ion concentration profiles conditioned on specific currents, extending understanding of ionic current fluctuations beyond Gaussian approximations.

Findings

Ionic current fluctuations are Gaussian at small voltages.

At large voltages, ionic current distribution becomes non-Gaussian.

Distribution structure is constrained by Gallavotti-Cohen symmetry and thermodynamic uncertainty principle.

Abstract

We evaluate the exponentially rare fluctuations of the ionic current for a dilute electrolyte by means of macroscopic fluctuation theory. We consider the fluctuating hydrodynamics of a fluid electrolyte described by a stochastic Poisson-Nernst-Planck equation. We derive the Euler-Lagrange equations that dictate the optimal concentration profiles of ions conditioned on exhibiting a given current, whose form determines the likelihood of that current in the long-time limit. For a symmetric electrolyte under small applied voltages, number density fluctuations are small, and ionic current fluctuations are Gaussian with a variance determined by the Nernst-Einstein conductivity. Under large applied potentials, where number densities vary, the ionic current distribution is generically non-Gaussian. Its structure is constrained thermodynamically by Gallavotti-Cohen symmetry and the thermodynamic uncertainty principle.