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For systems containing many particles (the thermodynamic limit), all three of the ensembles listed above tend to give identical behaviour. It is then simply a matter of mathematical convenience which ensemble is used. The Gibbs theorem about equivalence of ensembles was developed into the theory of concentration of measure phenomenon, which has applications in many areas of science, from functional analysis to methods of artificial intelligence and big data technology.

For systems containing many particles (the thermodynamic limit), all three of the ensembles listed above tend to give identical behaviour. It is then simply a matter of mathematical convenience which ensemble is used. The Gibbs theorem about equivalence of ensembles was developed into the theory of concentration of measure phenomenon, which has applications in many areas of science, from functional analysis to methods of artificial intelligence and big data technology.

对于包含大量粒子的系统(<font color="#FF8000">热力学极限 Thermodynamic Limit</font>) ，上面列出的三种系综都倾向于体现出相同的行为。因此，使用哪种系综只是一个简单的数学问题。发展成为(<font color="#FF8000">测度现象集中理论 Concentration of Measure Phenomenon</font>系综等价的吉布斯定理，在从函数分析到人工智能和大数据技术等许多科学领域都有广泛的应用。

对于包含大量粒子的系统(<font color="#FF8000">热力学极限 Thermodynamic Limit</font>) ，上面列出的三种系综都倾向于体现出相同的行为。因此，使用哪种系综只是一个简单的数学问题。发展成为<font color="#FF8000">测度现象集中理论 Concentration of Measure Phenomenon</font>系综等价的吉布斯定理，在从函数分析到人工智能和大数据技术等许多科学领域都有广泛的应用。