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. Patterns of distinct preferential pathways for fluid flow and solutetransport are ubiquitous in heterogeneous, saturated and partially saturatedporous media. Yet, the underlying reasons for their emergence, and theircharacterization and quantification, remain enigmatic. Here we analyzesimulations of steady-state fluid flow and solute transport intwo-dimensional, heterogeneous saturated porous media with a relativelyshort correlation length. We demonstrate that the downstream concentrationof solutes in preferential pathways implies a downstream declining entropyin the transverse distribution of solute transport pathways. This reflectsthe associated formation and downstream steepening of a concentrationgradient transversal to the main flow direction. With an increasing varianceof the hydraulic conductivity field, stronger transversal concentrationgradients emerge, which is reflected in an even smaller entropy of thetransversal distribution of transport pathways. By defining“self-organization” through a reduction in entropy (compared to itsmaximum), our findings suggest that a higher variance and thus randomness ofthe hydraulic conductivity coincides with stronger macroscaleself-organization of transport pathways. Simulations at lower driving headdifferences revealed an even stronger self-organization with increasingvariance. While these findings appear at first sight striking, they can beexplained by recognizing that emergence of spatial self-organizationrequires, in light of the second law of thermodynamics, that work beperformed to establish transversal concentration gradients. The emergence ofsteeper concentration gradients requires that even more work be performed,with an even higher energy input into an open system. Consistently, we findthat the energy input necessary to sustain steady-state fluid flow andtracer transport grows with the variance of the hydraulic conductivity fieldas well. Solute particles prefer to move through pathways of very high powerin the transversal flow component, and these pathways emerge in the vicinityof bottlenecks of low hydraulic conductivity. This is because power dependson the squared spatial head gradient, which is in these simulations largestin regions of low hydraulic conductivity.

Preferential pathways for fluid and solutes in heterogeneous groundwater systems: self-organization, entropy, work