Can hotter mantle have a larger viscosity?

In the diffusion creep regime which is believed to be appropriate for the lower mantle of the Earth, the viscosity of rocks depends on the grain size. The grain size is normally assumed to be constant in mantle convection models. However, it is controlled by the kinetics of polymorphic phase transformations and post‐transformation grain growth and can vary substantially. A simple scaling analysis demonstrates one particular feature of the interaction of rheology, convection and kinetics: the mantle resembles a temperature‐dependent viscosity fluid with an extremely unusual apparent activation enthalpy for the viscosity. It can take almost any value including negative so that hotter regions can have a larger viscosity or the averaged viscosity of the mantle can increase during Earth's secular cooling. This affects mantle dynamics and evolution and should also be taken into account in interpretating the viscosity variations in the mantle.