Large deviations of ionic currents in dilute electrolytes

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.