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. Majorization, a tool originating in economics that has found utility in statistical mechanics, can provide insight into how Leontief analysis links disparities in emissions with global income inequality. We examine Leontief analysis as a model, drawing out similarities with modern 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 emission flows. Surprisingly, relatively small trade deficits and a geographically heterogeneous emissions-per-dollar ratio greatly increases 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, based on data provided by the Global Trade Aggregation Project9