Reversible heating in electric double layer capacitors

A detailed comparison is made between different viewpoints on reversible heating in electric double layer capacitors. We show in the limit of slow charging that a combined Poisson-Nernst-Planck and heat equation, first studied by d'Entremont and Pilon [J. Power Sources {\bf 246}, 887 (2014)], recovers the temperature changes as predicted by the thermodynamic identity of Janssen, H\"{a}rtel, and van Roij [Phys. Rev. Lett. {\bf 113}, 268501 (2014)], and disagrees with the approximative model of Schiffer, Linzen, and Sauer [J. Power Sources {\bf 160}, 765 (2006)] that predominates the literature.