Multidimensional Urban Shrinkage–Carbon Emission Efficiency Nexus at the Patch Scale: Spatiotemporal Evolution, Nonlinear Impacts, and SSP Scenario Projections

Abstract Urban shrinkage, a global phenomenon characterized by population decline and economic contraction, remains underexplored regarding its correlation with carbon emission efficiency (CEE). This study utilizes multisource geographic big data, the undesirable slack-based measure model, and Bayesian networks to analyze the spatiotemporal evolution and interaction mechanisms of shrinkage and CEE in China. The results indicate that (1) shrinkage patterns shifted from population dominance in 2010 to society dominance in 2015 and economy dominance in 2020, with the number of shrinking patches increasing from 599 to 2,857 and northeast China reaching a 64.97% shrinkage proportion; (2) CEE improved consistently, with high-efficiency patches surging from 10.8% in 2010 to 56.9% in 2020, revealing a distinct north–south spatial divergence; (3) multidimensional shrinkage exhibits complex nonlinear impacts on efficiency, in which population shrinkage follows an N-shaped trajectory, economy shrinkage shows an inverted U-shaped influence, and society shrinkage presents a U-shaped pattern; (4) future projections under scenarios of Shared Socioeconomic Pathways (SSP) for 2050 suggest that population shrinkage will intensify and economy shrinkage will alleviate, while society shrinkage indices are projected to rebound by approximately 18.6 units from the baseline, with CEE surging 4.3–4.5 times driven by systemic technological advancements and passive efficiency gains from resource consolidation; and (5) spatial optimization identifies 3,805 patches requiring intervention, primarily clustered in north and northeast regions. Theoretically, this study enhances the understanding of nonlinear shrinkage–CEE dynamics, and practically, it informs targeted low-carbon zoning policies for shrinking cities.