Large deviations of ionic currents in dilute electrolytes

Jafar Farhadi; David T. Limmer

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arXiv · 2507.18556

Large deviations of ionic currents in dilute electrolytes

Jafar Farhadi·David T. Limmer

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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.

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Jafar Farhadi, David T. Limmer. 2025-07-24. Large deviations of ionic currents in dilute electrolytes. https://arxiv.org/abs/2507.18556

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