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The electrostatic screening properties of ionic fluids are of paramountimportance in countless physical processes. Yet, the behavior of ionicconductors out of thermal equilibrium has to date mainly been studied in thecontext of thermodiffusion phenomena by virtue of direct extensions ofDebye-H\"uckel theories. We investigate how the static response of a symmetricionic fluid is influenced by the presence of a thermal gradient by introducinga theory of electrostatic screening under a stationary temperature profile. Byborrowing mathematical methods commonly used in the semiclassical approximationof quantum particles, we find analytical solutions to the asymptotic decay ofthe charge density which can be used to describe the non-equilibrium responseof the system to external charge perturbations and for arbitrary ionicconcentrations. Notably, a transition between monotonic and oscillatoryscreening regimes is observed as an effect of the temperature variation whichgeneralizes known results of thermal equilibrium to out of equilibriumconditions. A final quantitative example on the screening of charged surfacesin aqueous electrolytes shows that the deviation from thermal equilibriumpredicted by our solutions is generally larger than thermodiffusion effects,and should therefore be taken into account for a comprehensive description ofthe electrical double layer. Our findings pave the way to the rigoroustreatment of non-equilibrium steady states in ionic systems with potentialapplications to the study of energy materials, nanostructured systems andwaste-heat-recovery technologies.

Effect of a Temperature Gradient on the Screening Properties of Ionic Fluids