Hill relationship for temperature dependence: An alternative to Arrhenius formalism

The Arrhenius relationship has been the staple for description of the temperature dependence of physical properties. Here, the Hill relationship is presented that can be an alternative to the Arrhenius formalism for those cases where the formalism fails. The Hill relationship is based on the Hill probability function. The probability functions in both relationships, Arrhenius and Hill, have the same single argument. The resistances of lithium ion batteries, not obeying the Arrhenius dependence, are shown to be adequately represented by the Hill relationship. The viscosities of various liquid foods, deviating from the Arrhenius formalism, are also demonstrated to be adequately described by the Hill formalism. These results suggest that the Hill relationship could serve well for representing the temperature dependence of physical properties.