  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
