The Arrhenius equation says the rate of spoilage rises exponentially with temperature: k = A x exp(-Ea/RT). Ea is the activation energy, specific to the product and its dominant spoilage reaction; it is extracted from shelf life measured at two or, better, three temperatures, and estimates are then made for temperatures in between.
A published example: HPP-preserved fruit smoothies were followed for 24 days at 5, 10 and 15 °C; the rise in total aerobic count gave Ea of 13.7 kcal/mol (about 57 kJ/mol), and the Arrhenius estimate came out at about 57 days at 5 °C and about 50 days at 7 °C. Two degrees more in the chain took about 7 days off the life.
The limit is this: the model works only where a valid kinetic model exists and the same spoilage reaction stays dominant. Producing estimates for other temperatures from a study at a single temperature is an assumption, not a calculation. In the field, a temperature record is turned into a remaining-life estimate by weighting the time spent at each temperature with the rate factor for that temperature and summing.
