Kavli Affiliate: David T. Limmer
| First 5 Authors: Jafar Farhadi, Jafar Farhadi, , ,
| Summary:
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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