Entropy increase principle in isolated system, which is deduced from the discussion of Clausius entropy and Boltzmann entropy, has further deduced entropy principle in open system as well.
通过对克劳修斯熵、玻耳兹曼熵的讨论，得到熵的本质和孤立系统的熵增加原理，并把孤立系统的熵增加原理推广为开放系统的熵原理。
So, Boltzmann understood that and he explained how entropy is related to the arrow of time.
所以，波尔兹曼了解这一点并且他解释了熵是如何与时间之箭相关的。
So we could get this result from another pathway, too, but a more simple and direct way is just to start directly from the Boltzmann result for entropy.
所以我们也能从另一途径得到这个结果，但一个更简单，更直接的方式是直接，从波耳兹曼的结果入手得到熵。
There are surprising applications of these concepts in the maximum entropy distribution, which tells us how to build "least clustered" networks according to the Boltzmann distribution.
在最大熵分布中有这些概念的一些应用，这告诉我们如何根据Boltzmann分布构建“最小聚集”网络。
Using a method that do not relate to the concrete system, the Clausius entropy expression is deduced from the Boltzmann relation and information entropy.
由不涉及具体系统的方法从玻尔兹曼关系、信息熵推导出了克劳修斯熵的表达式；
The article introduced the definition of Clausius entropy and Boltzmann s entropy, then proved Clausius entropy from the Boltzmann s entropy, and explained the unity of two kinds of entropy.
文章先分别介绍了克劳修斯熵与玻耳兹曼熵的定义，然后以玻耳兹曼系统为例，从玻耳兹曼熵到克劳修斯熵进行了推导，从而论述了两种熵的统一。
The analysis on the entropy equation shows that the BGK Boltzmann equation meets the entropy condition strictly, implying that the BGK method meets the entropy condition.
通过对熵方程分析表明，BGK波尔兹曼方程严格满足熵条件，从而阐释了BGK模拟方法满足熵条件。
Boltzmann: the increase in entropy in an equalization process is the result of the system passing from a less probable states to the most probable state.
平衡化过程熵的增加是系统从较少几率态到较多几率态变化的结果。
Using a simple method, this paper established a Boltzmann relation on entropy.
本文用一种简单的方法建立了熵的玻尔兹曼关系式。
Using a simple method, this paper established a Boltzmann relation on entropy.
本文用一种简单的方法建立了熵的玻尔兹曼关系式。
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