Weathering reactions and isometric log-ratio coordinates: Do they speak to each other?

The aim of this contribution is to explore the relationship among some concepts, often considered to be unrelated, such as weathering reactions, compositional data and fractals by means of distribution analysis. Weathering reactions represent the necessary transfer of heat and entropy to the environment in geochemical cycles. Compositional data express the relative abundance of chemical elements/species in a given total (i.e. volume or weight). Fractals are temporal or spatial objects with self-similarity and scale-invariance, so that internal structures repeat themselves over multiple levels of magnification or scales of measurement. Gibbs's free energy and the application of the Law Mass Action can be used to model weathering reactions, under the hypothesis of chemical equilibrium. Compositional data are obtained in the analytical phase after the determination of the concentrations of chemicals in sampled solid, liquid or gaseous materials. Fractals can be measured by using their fractal dimensions. In this paper, the presence of fractal structures is observed when the frequency distribution of isometric log-ratio coordinates is investigated, showing the logarithm of the cumulative number of samples exceeding a certain coordinate value plotted against the coordinate value itself. Isometric log-ratio coordinates (or balances) were constructed by using the sequential binary partition (SBP) method. The balances were identified to maintain, as far as possible, the similarity with a corresponding weathering reaction affecting the Arno river catchment (Tuscany, central Italy) as described by the Law of Mass Action. The emergence of fractal structures indicates the presence of dissipative systems, which require complexity, large numbers of inter-connected elements and stochasticity.