Thermodynamics, maximum power, and the dynamics of preferential river flow structures at the continental scale

The organization of drainage basins shows some reproducible phenomena, as exemplified by self-similar fractal river network structures and typical scaling laws, and these have been related to energetic optimization principles, such as minimization of stream power, minimum energy expenditure or maximum access. Here we describe the organization and dynamics of drainage systems using thermodynamics, focusing on the generation, dissipation and transfer of free energy associated with river flow and sediment transport. We argue that the organization of drainage basins reflects the fundamental tendency of natural systems to deplete driving gradients as fast as possible through the maximization of free energy generation, thereby accelerating the dynamics of the system. This effectively results in the maximization of sediment export to deplete topographic gradients as fast as possible and potentially involves large-scale feedbacks to continental uplift. We illustrate this thermodynamic description with a set of three highly simplified models related to water and sediment flow and describe the mechanisms and feedbacks involved in the evolution and dynamics of the associated structures. We close by discussing how this thermodynamic perspective is consistent with previous approaches and the implications that such a thermodynamic description has for the understanding and prediction of sub-grid scale organization of drainage systems and preferential flow structures in general.