Multiregional input-output (MRIO) tables, in conjunction with Leontief analysis, are widely-used to assess the geographical distribution of carbon emissions and the economic activities that cause them. We examine Leontief analysis as a model, demonstrating commonalities with modern approaches in information theory and nonequilibrium statistical mechanics. Paralleling the physical concept of thermo-majorization, we define the concept of eco-majorization and show it is a sufficient condition to determine the directionality of embodied impact flows. Surprisingly, relatively small trade deficits and geographically heterogeneous impacts greatly increase the appearance of eco-majorization, regardless of any further content in the MRIO tables used. Our results are bolstered by a statistical analysis of null models of MRIO tables developed by the Global Trade Aggregation Project.