纯系综和混合系综的大偏差原理和完全等价与不等价结果
Large Deviation Principles and Complete Equivalence and Nonequivalence Results for Pure and Mixed Ensembles
摘要：
我们考虑一类湍流相干结构的统计力学模型，其中包括二维流体运动，准地转流和色散波的模型。首先证明了正则系综和微正则系综的大偏差原理。对于每个系综，平衡宏观态的集合被定义为相应的速率函数达到其最小值0的集合。然后，我们提出了完全等价和不等价的结果在平衡宏观态的水平上的两个合奏。
英文摘要：
We consider a general class of statistical mechanical models of coherent structures in turbulence, which includes models of two-dimensional fluid motion, quasi-geostrophic flows, and dispersive waves. First, large deviation principles are proved for the canonical ensemble and the microcanonical ensemble. For each ensemble the set of equilibrium macrostates is defined as the set on which the corresponding rate function attains its minimum of 0. We then present complete equivalence and nonequivalence results at the level of equilibrium macrostates for the two ensembles.
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