Quantifying mantle mixing through configurational entropy

Geodynamic models of mantle convection provide a powerful tool to obtain insights into the structure and composition of the Earth's mantle that resulted from a long history of differentiating and mixing. Comparing such models with geophysical and geochemical observations is challenging, as these datasets often sample entirely different temporal and spatial scales. Here, we explore the use of configurational entropy, based on tracer and compositional distribution on a global and local scale. We show means to calculate configurational entropy in a 2D annulus and find that these calculations may be used to quantitatively compare long-term geodynamic models with each other. The entropy may be used to analyse, with a single measure, the mixed state of the mantle as a whole and may also be useful to compare numerical models with local anomalies in the mantle that may be inferred from seismological or geochemical observations.