Impact of population mobility and urban resource allocation on the size distribution of cities

The kinetic theory is applied to investigate the impact mechanism of population mobility and urban resources on the evolution of city size distribution. The formation and transformation of city size are not the result of a single factor, but are influenced by multiple variables such as population mobility, resource endowments, and living environments. To systematically analyze the dynamic evolution law of city size distribution, we construct a Boltzmann model that integrates Markov transition probability and value function. This model not only incorporates the probability characteristics of population transfer between different cities (characterizing the randomness and directionality of population mobility), but also describes various factors that affect population migration by using a suitable value function, thus more accurately capturing the impact path of population migration behavior on city size. With the help of this Boltzmann model, we simulate and analyze the evolution process of city size distribution, ultimately revealing how population migration patterns and urban resource allocation interact to promote the specific evolution trend of city size distribution.