Abstract:

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.

Key words: thermostatistics, ensemble, statistical distribution, equivalence