The long term dirft has multiple contributions and not all have the same temperature dependence. The can also be oppsing effects, so that a relatively small error in one contribution can cause a large error in the final sum. Quite often one of the porcesses dominates, but this does not mean that the slower processes are not happening and get relevant for the really long time scale. The relative relevance can change with time (aging) and temperature.
One sometimes sees this on the short time scale with the drift rate even changing the sign.
The Arrhenius type thermal activation with processes speeding up exponential is just one possible describtion. Even here there can be different activation energies and thus a different temperature difference to cause a doubling in the speed. For interpolation over a small temperature range this may still be OK, but with a larger temperature step this can cause significant errors.
An important type of aging that often follows a different equation is the relaxation of mechnical stress: there the creep rate also depends some power of the stress and the stress from thermal mismatch changes with temperature. There is often still an exponential factor from thermal activation, but only as one part of the quation.
Also glassy materials (e.g. epoxy) relatively close to the glass transition are known to behave different: there sturcture changes with temperature and this can effects the speed of other processes, like diffusion of oxigen and stress relaxation.
Another formular used that is not necessary correct is the square root time dependence. This is valid for a simple diffusion processes and random walk like processes, but not necessary all aging processes. Other effects can follow a simple exponential decay or stretched exponential with a power different from 2.
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