2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/224992We investigate the quasi-potential problem for the entropy cost functionals of non-entropic solutions to scalar conservation laws with smooth fluxes. We prove that the quasi-potentials coincide with the integral of a suitable Einstein entropy.26 pages, 4 figuresAnalysis of PDEsOptimization and Control35L65; 49S05text