Gravity-Model Estimates and Exact Maximum-Entropy Solutions: Their Differences

• https://journals.sagepub.com/doi/abs/10.1068/a101131

Gravity model of mobility, Principle of maximum entropy

The “standard distribution problem” assumes the three constraints. The total number of workers who live in $i$ ($\sum_j T_{ij} = O_i$), the total number of jobs in $j$ ($\sum_i T_{ij} = D_j$), and the total expenditure on travel to work ($\sum_i \sum_j T_{ij}c_{ij} = C$). The gravity law emerges as the Principle of maximum entropy solution.