Least action principle (LAP) in rivers is demonstrated by maximum flow efficiency (MFE) and is the foundation of variational
mechanics based on energy and work rather than Newtonian force and momentum. Empirical evidence shows it to be the
primary control for the adjustment of alluvial channels. Because most rivers flow with imposed water and sediment loads down valley
gradients they have largely inherited, they self-regulate energy expenditure to match the work they are required to do to remain stable.
Overpowered systems develop a variety of channel patterns to expend excess energy and remain stable. Australia offers an opportunity
to study low-energy rivers closely adjusted to very low continental gradients. The anabranching Marshall and single-thread Plenty
Rivers flow down nearly straight channels with average H numbers [ratio between excess bed shear and width/depth (W/D) ratio]
close to the optimum of 0.3 for stationary equilibrium. Ridge-form divisions of the original channel width create anabranches that radically
alter W/D ratios relative to bed shear, the same being true for short-wide islands on the large low-gradient Yangtze River in
China. In contrast, Mount Chambers Creek in Australia’s tectonically more active Flinders Ranges is accreting an alluvial fan with unstable
distributary channels exhibiting H numbers well below the optimum. LAP also explains profound biases in Earth’s stratigraphic
record. Because meandering is an energy-shedding mechanism, sinuous rivers sequester relatively little sediment resulting in all sequences
being just a few tens of metres thick. In contrast, low-energy braided disequilibrium systems can sequester sediment piles
over a kilometre in thickness and tens of kilometres wide. LAP provides a new paradigm for river research by identifying the attractor
state controlling river channel evolution. It links advances in theoretical physics to fluvial geomorphology, stratigraphy and hydraulic
engineering and opens opportunities for diverse investigations in Earth system science.