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Abstract The zonal gradients in sea surface temperature and convective heating across the tropical Pacific play a pivotal role in setting the weather and climate patterns globally. Under global warming, the current generation of climate models predict that the zonal gradients will decrease, but the trajectory of the observed trends is the opposite. Theories supporting either of the two projections exist, but there are many relevant processes whose net effect is unclear. In this study, a global constraint – the maximum material entropy production (maxMEP) hypothesis—is considered to help close the gap. The climate system considered here is comprised of a one-layer atmosphere and surface in six regions that represent the western tropical Pacific, eastern tropical Pacific, northern and southern midlatitudes, and northern and southern polar regions. The model conserves energy but does not explicitly include dynamics. The model input is observation-based radiative parameters. The radiative effect of greenhouse gas (GHG) loading is mimicked by prescribing increases in the longwave absorptivity$$\epsilon$$ $ϵ$. The model solutions predict that zonal contrasts in surface temperature, convective heat flux, and surface pressure increase with increasing$$\epsilon$$ $ϵ$. While maxMEP solutions in general cannot provide a definite answer to the problem, these model results strengthen the possibility that the trajectory of the observed trend reflects the response to increasing GHG loading in the atmosphere.