Cumulative thermal destruction under exponential warming and cooling ($D(T)={\beta }_{\max }[T-e^{-\alpha T}(1-e^{-\alpha T})/\alpha ]$)

In an ideal linear temperature-dependent destruction model with equal warming and cooling durations, normalized temperature is $1-e^{-\alpha t}$ during warming and $(1-e^{-\alpha T})e^{-\alpha (t-T)}$ during cooling. Integrating the destruction rate gives $D(T)$, the logarithm of the surviving-count reduction factor. If the endpoint destruction rate and thermal relaxation constant stay fixed, changing the temperature gap alone leaves this integral unchanged. This is a property of the stipulated model.