Asymptotic Behavior of a Sequence of Conditional Probability Distributions and the Canonical Ensemble
Asymptotic Behavior of a Sequence of Conditional Probability Distributions and the Canonical Ensemble
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DOI：
10.1007/s00023-020-01011-2
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发表时间：
2019-12
期刊：
影响因子：
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通讯作者：
Yu-Chen Cheng;H. Qian;Yizhe Zhu
中科院分区：
文献类型：
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作者：
Yu-Chen Cheng;H. Qian;Yizhe Zhu
子系统的函数的概率分布以整体函数的值为条件，在它们的值之比趋于零的极限中，具有极限定律：它等于由指数因子加权的无条件边际概率分布，该指数因子的指数由条件唯一确定。我们应用这个定理来解释与热源接触的系统的正则平衡系综。由于该定理只需要在子系统和水库的功能水平上进行分析，因此即使不知道水库本身的组成，它也是适用的，这扩展了正则系综的适用性。此外，我们将我们的定理推广到具有强相互作用的模型，该模型对指数贡献了额外的项，这超出了近似可加函数的典型情况。这个结果在物理学和数学上都是新的，作为强关联系统的吉布斯条件原理的理论。一个推论提供了一个精确的公式是什么温度浴在概率方面。
The probability distribution of a function of a subsystem conditioned on the value of the function of the whole, in the limit when the ratio of their values goes to zero, has a limit law: It equals the unconditioned marginal probability distribution weighted by an exponential factor whose exponent is uniquely determined by the condition. We apply this theorem to explain the canonical equilibrium ensemble of a system in contact with a heat reservoir. Since the theorem only requires analysis at the level of the function of the subsystem and reservoir, it is applicable even without the knowledge of the composition of the reservoir itself, which extends the applicability of the canonical ensemble. Furthermore, we generalize our theorem to a model with strong interaction that contributes an additional term to the exponent, which is beyond the typical case of approximately additive functions. This result is new in both physics and mathematics, as a theory for the Gibbs conditioning principle for strongly correlated systems. A corollary provides a precise formulation of what a temperature bath is in probabilistic terms.