勒让德变换是理论物理学中一个重要的工具，多变量函数的勒让德变换有明显的对称性. 系综是统计力学教学中 的核心内容. 利用勒让德变换的无量纲性，从微正则系综的特性函数熵的勒让德变换出发，类比的定义了配分函数的勒让德 变换. 同时得到各种系综的特性函数和配分函数以及它们之间的关系和相应的热力学公式.

The Legendre transform is an important tool in theoretical physics，and the Legendre transform of multivariable function has manifestly symmetry. Ensemble is the core content of statistical mechanics. Using the dimensionless of Legendre transform，the Legendre transform of partition function can be analogy definition from the Legendre transform of entropy，which is characteristic function of microcanonical ensemble. Meanwhile，the characteristic function， partition function of every ensemble and their relations as well as the relevant thermodynamics formula，can be obtained.