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Large deviations of ionic currents in dilute electrolytes.

Jafar Farhadi1, David T Limmer2,3,4,5

  • 1Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California 94720, USA.

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|October 24, 2025
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Summary
This summary is machine-generated.

We analyzed rare ionic current fluctuations in electrolytes using macroscopic fluctuation theory. Results show current fluctuations are Gaussian for small voltages but non-Gaussian for large potentials, revealing thermodynamic constraints.

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Area of Science:

  • Physical Chemistry
  • Chemical Physics
  • Theoretical Chemistry

Background:

  • Ionic current fluctuations are crucial for understanding electrolyte behavior.
  • Macroscopic fluctuation theory provides a framework for analyzing rare events.
  • Stochastic Poisson-Nernst-Planck equations model fluid electrolyte hydrodynamics.

Purpose of the Study:

  • To evaluate exponentially rare fluctuations of ionic current in dilute electrolytes.
  • To derive optimal ion concentration profiles for specific current values.
  • To investigate the transition from Gaussian to non-Gaussian current distributions.

Main Methods:

  • Application of macroscopic fluctuation theory.
  • Modeling fluid electrolytes with stochastic Poisson-Nernst-Planck equations.
  • Derivation of Euler-Lagrange equations for optimal concentration profiles.

Main Results:

  • For small applied voltages, ionic current fluctuations are Gaussian, with variance linked to Nernst-Einstein conductivity.
  • Under large applied potentials, ionic current distributions become non-Gaussian.
  • The structure of current fluctuations is thermodynamically constrained by Gallavotti-Cohen symmetry and the thermodynamic uncertainty principle.

Conclusions:

  • The study elucidates the statistical behavior of ionic current fluctuations in electrolytes.
  • It highlights the importance of applied voltage in determining fluctuation characteristics.
  • Thermodynamic principles play a key role in constraining these fluctuations.