The braess paradox model is taken as an example to reveal the essence of entropy - maximization and utility - maximization which lies in the unity of the most efficient for the whole and the fairest for local parts and individuals . the internal symmetry of the scaling laws are bring to light based on the dual model of entropy - and utility - maximization . the internal symmetry including translational symmetry , dilation symmetry , and bilateral symmetry originate from relative energy - conservation and information conservation of urban systems reflected by the dual models , and parity conservation of scaling laws 揭示标度律及其等价模型各种对称性质,发现城市系统具有平移对称、镜像对称和标度对称等内部对称性,这些对称性都对应着城市系统的不可观测量,其本质在于系统内部隐含的守恒律,包括标度变换的奇偶守恒、能量和信息的相对守恒等。
