  Several modern technologies for energy storage and conversion are based on
the screening of electric charge on the surface of porous electrodes by ions in
an adjacent electrolyte. This so-called electric double layer (EDL) exhibits an
intricate interplay with the electrolyte's temperature that was the focus of
several recent studies. In one of them, Janssen et al. [Phys. Rev. Lett. 119,
166002 (2017)] experimentally determined the ratio
$\mathcal{Q}_\text{rev}/W_\text{el}$ of reversible eat flowing into a
supercapacitor during an isothermal charging process and the electric work
applied therein. To rationalize that data, here, we determine
$\mathcal{Q}_\text{rev}/W_\text{el}$ within different models of the EDL using
theoretical approaches like density functional theory (DFT) as well as
molecular dynamics simulations. Applying mainly the restricted primitive model,
we find quantitative support for a speculation of Janssen et al. that steric
ion interactions are key to the ratio $\mathcal{Q}_\text{rev}/W_\text{el}$.
Here, we identified the entropic contribution of certain DFT functionals, which
grants direct access to the reversible heat. We further demonstrate how
$\mathcal{Q}_\text{rev}/W_\text{el}$ changes when calculated in different
thermodynamic ensembles and processes. We show that the experiments of Janssen
et al. are explained best by a charging process at fixed bulk density, or in a
"semi-canonical" system. Finally, we find that
$\mathcal{Q}_\text{rev}/W_\text{el}$ significantly depends on parameters as
pore and ion size, salt concentration, and valencies of the cat- and anions of
the electrolyte. Our findings can guide further heat production measurements
and can be applied in studies on, for instance, nervous conduction, where
reversible heat is a key element.
