第四统计力学-JRG群子统计理论的现状与展望

1978年,作者首次发表了群子统计理论及其在某些自然科学领域里应用的论文;接着于1984年出版了“模糊群子论”,系统地论述了线性群子理论方程及其某些应用。而后又把群子理论推广到群子间相互作用的非线性体系中,建立了重整化非线性群子理论方程。这些理论不仅能够推导出Fermi-Dirac,Bose-Einstein,Maxwell-Boltzmann统计方程,而且用很简单的方法可推导出著名的Van der Waals非理想气体方程,Kohlrausch电导方程,BET多层吸附方程。通过非线性群子方程又推导了汽液平衡组成关系式,高分子溶液第二维利系数与分子量之间的关系式,共聚物玻璃化温度与组成关系,高分子合金熔体粘度与组成关系,分子量分布关系式等。这些都表现了第四统计理论在各方面的普遍适用性和广泛应用的前景。

The Status and the Prospect of the Fourth Statistic Theory-JRG Sub-Cluster Statistics

The first paper of the author on the sub-cluster statistics and its application in some fields of natural science was published in 1978. Then in 1984, "On Vague Sub-cluster", which systematically, expounded the linear sub-cluster equation and its application, was off the press. Afterwards, the sub-cluster statistics was extenoed to the non-linear systems in which the sub-clusters interacted with one another and the reformational non-linear sub-cluster equation was established. From these theories, not only can the Fermi-Dirac, Bose-Einstein and Maxwell-Boltzmann statistics be derived but also a few of wellknown equations, such as Van der Waals equation for non-ideal gas Kohlrausch conductivity equation for the electrolytic solution, and BET equation for isothermal adsorption can be deduced via a rather simple process From the non-linear sub-cluster equation, a new vapor-liquid equilibrium equation, the relationship of the second Virial Cefficient for polymer solution and the molecular weight, the dependence of glass transition temperature, melt viscosity on the composition, and the molecular weight distribution, etc. had been obtained. All of thesese has displayed the universal applicability and the prospect for the wide-range appliance of the fourth statistic theory.