Wasserstein Gradient Flow Optimization and Unequal Convergence Mechanism for Social and Economic Resource Spatial Allocation

In response to the theoretical limitations of traditional spatial economics in depicting heterogeneous spatial frictions, this paper breaks away from the comparative static analysis framework and innovatively introduces the optimal transport theory to construct a dynamic evolution model of resource spatial allocation based on the Wasserstein gradient flow. Mathematical derivations show that under the strong constraints of non-convex energy fields and spatial frictions, weak initial endowment differences will trigger the symmetry breaking of the system's evolution path; resource flow consumes virtual kinetic energy in overcoming high institutional and physical barriers, and inevitably falls into a local minimum trap, ultimately solidifying into a non-equilibrium spatial steady state of "core-periphery" on a macro scale. Further, relying on the time-discrete JKO variational format and entropy regularization calculation framework, this paper accurately reproduces the entire life cycle of the system's collapse from a homogeneous state to a polarized state on a two-dimensional grid, and quantitatively decomposes the bifurcation boundary between the constraining effect of spatial barriers and the topological phase transition of agglomeration. This research provides a macro governance approach with solid mathematical support and quantitative decision-making value for breaking administrative division barriers at the national level, crossing spatial lock-in traps, and building a unified national market.