在统计物理理论中，因为在传统理论中有系综等价的严格证明，因而人们通常习惯于使用等价的思想方法做一些理论工作，以及选择最便于计算的系综来研究热力学性质.正则系综最便于理论计算，微正则系综最便于数值计算，巨正则系综计算量子气体的热力学性质最简单，因此，现有的新老教材中一般只讲这三种系综.但早在1970 年有学者提出在相变点附近具有长程相互作用的系统正则系综与微正则系综不等价，近年又有学者提出此时短程相互作用的系统两系综也可不等价，且不等价的研究成果越来越多.因而更新观念和统计热力学教材势在必行.本文仅以一平均变量之间存在关联的简单系统为 例，说明这种“关联”也会导致系综不等价.

In statistical physics theory，once ones thought different ensembles to be equivalent，because equivalence of ensembles had been proven rigorously in the traditional theory. Therefore，ones use equivalent thought methods to do some theoretical work，and select the most computationally convenient ensemble to study the thermodynamic properties. Canonical ensemble is the most convenient for theoretical calculation，the microcanonical ensemble is the most convenient for numerical calculation，and the grand canonical ensemble is the most convenient to calculate the thermodynamic properties of quantum systems. Therefore，the existing new and old textbooks generally only talk about these three ensembles. However，in the 1970s，some researchers proposed that the canonical ensemble is nonequivalent to the microcanonical ensemble for systems with long-range interactions in the vicinity of phase transition point. In recent years，some scholars suggested that the two ensembles are also nonequivalent for systems with short-range interactions in the vicinity of phase transition point，and more and more research results show that

ensemble is nonequivalent. Therefore，it is imperative to update concepts and statistical thermodynamics textbooks. In this paper，a simple system with correlative average variables is taken as an example，which indicates that this "correlation" can also lead to the nonequivalence of the ensemble.