The crystallographic structure of solid electrolytes and other materials determines the protonic conductivity in devices such as fuel cells, ionic-conductors, and supercapacitors. Experiments show that a rise of the temperature in a narrow interval may lead to a sudden increase of several orders of magnitude of the conductivity of some materials, a process called a superprotonic transition. Here, we use a novel macro-transport theory for irregular domains to show that the change of entropic restrictions associated with solid-solid phase or structural transitions controls the sudden change of the ionic conductivity when the superprotonic transition takes place. Specifically, we deduce a general formula for the temperature dependence on the ionic conductivity that fits remarkably well experimental data of superprotonic transitions in doped cesium phosphates and other materials reported in the literature.