<p>While a sustained contraction of global production could lower total carbon emissions, it would hamper economic development in poorer countries, reduce living standards for low-income households in advanced economies, and heighten the risk of social unrest. Therefore, reducing carbon intensity – emissions per unit of output – appears to be the most viable and sustainable path forward. We make two contributions: one empirical and one theoretical. Empirically, we show that the transport equation, a basic partial differential equation from physics, captures well the evolution of the distribution of carbon intensities across major economies since 1995. Theoretically, we show that in an extended Solow model with abatement capital, the distribution of carbon intensity across a continuum of economies follows the dynamics described by the transport equation. Moreover, this theory-backed version remains empirically plausible under standard parameter values. In addition, unlike its empirical counterpart, it enables projections of emissions and temperature increases under various policy scenarios, aligning closely with forecasts by leading institutions.</p>