Large deviations of ionic currents in dilute electrolytes
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912499912146944 |
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| author | Farhadi, Jafar Limmer, David T. |
| author_facet | Farhadi, Jafar Limmer, David T. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_18556 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Large deviations of ionic currents in dilute electrolytes Farhadi, Jafar Limmer, David T. Statistical Mechanics Mesoscale and Nanoscale Physics Chemical Physics 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. |
| title | Large deviations of ionic currents in dilute electrolytes |
| topic | Statistical Mechanics Mesoscale and Nanoscale Physics Chemical Physics |
| url | https://arxiv.org/abs/2507.18556 |