  We introduce a new quantity to petrology, the Shannon entropy, as a tool for
quantifying mixing as well as the rate of production of hybrid compositions in
the mixing system. The Shannon entropy approach is applied to time series
numerical simulations and high-temperature experiments performed with natural
melts. We note that in both cases the Shannon entropy increases linearly during
the initial stages of mixing and then saturates toward constant values.
Furthermore, chemical elements with different mobilities display different
rates of increase of the Shannon entropy. This indicates that the hybrid
composition for the different elements is attained at different times
generating a wide range of spatio-compositional domains which further increase
the apparent complexity of the mixing process. Results from the application of
the Shannon entropy analysis are compared with the concept of Relaxation of
Concentration Variance (RCV), a measure recently introduced in petrology to
quantify chemical exchanges during magma mixing. We derive a linear expression
relating the change of concentration variance during mixing and the Shannon
entropy. We show that the combined use of Shannon entropy and RCV provides the
most complete information about the space and time complexity of magma mixing.
As a consequence, detailed information about this fundamental petrogenetic and
volcanic process can be gathered. In particular, the Shannon entropy can be
used as complement to the RCV method to quantify the mobility of chemical
elements in magma mixing systems, to obtain information about the rate of
production of compositional heterogeneities, and to derive empirical
relationships linking the rate of chemical exchanges between interacting magmas
and mixing time.
