Entropy, fractality, and thermodynamics of groundwater pathways

This Work deepens the issue of groundwater connectivity and the behavior of permeable (alluvial) pathways from a thermodynamic viewpoint. Groundwater pathways have been inferred from geological data upon a starting dataset of 2000 MC simulations of alluvial sediment ratios. Each MC-realization is thresholded upon a certain sediment's ratio threshold, within the unit interval. Each ensemble of connected locations forms a sub-surface pathway, and the latter is fitted through a Gibbs' Distribution (GD). Each distribution's best-fit exponent is proportional to the local entropy in a random point of the connected pathway. GD's exponents decrease at the increase of the threshold prescribed for defining an alluvial pathway, proving that a higher conductivity threshold enables identifying a highly efficient pathway, where groundwater flow encounters less resistance, tending to be more conveyed. Moreover, more probable pathways return lower GD exponents. Lower GD ex-ponents imply a lower energy dissipation within a groundwater pathway; hence the latter is thermodynamically more efficient (and colder) than its less probable counterparts. Moreover, most probable groundwater pathways are close to a thermodynamical equilibrium (zero free-energy), making their spatial (probable) structure more ordered to energetic fluctuations. In addition, the estimation of GD's exponents for a randomly sampled con-nected pathways subset enables to highlight the fractal nature of a subsurface pathway; the GD's exponent weak variation across scales underlines its role as a signature of the whole pathway as of its portions. These results, achieved only from geological data, are important for understanding the patterns of ground-water and contaminant pathways and are strikingly consistent with the latest findings of the research in hy-drological systems thermodynamics. This work frames groundwater pathways' delineation within a novel thermodynamic framework and reconciles their spatial behavior to that of their surface counterparts.