论世界宗教信仰分布的演变
On World Religion Adherence Distribution Evolution
摘要：
从统计物理学的意义上讲，宗教信仰可以被认为是属于某个群体的人类主体的自由度。因此，宗教的分布，性能和生命周期可以研究考虑异构交互代理建模。我们提出了一个全面的分析58所谓的宗教（将在正文中更好地定义）演变，通过1900年至2000年之间的信徒数量来衡量-数据来自世界基督教百科全书：40个被认为是“目前正在增长”的案例，包括XX世纪的11个转变; 18个是“目前正在衰变”，其中12个被发现在XIX或XX世纪有最近的最大值。在每种情况下使用的Avrami-Kolmogorov微分方程，它通常描述固态变换，如晶体生长，以获得先前介绍的优先连接参数。它经常被发现接近统一，表明一个平稳的演变。然而，大的值表明发生的极端情况下，我们推测是由所谓的外部领域。少数病例显示类似于分离过程。我们讨论不同的成长和衰落的宗教，并说明各种适合。有些情况似乎表明数据缺乏可靠性。其他人，背离阿夫拉米法。我们指出两个困难的分析：（一）“精确”的原始时间的幽灵的宗教，（ii）的时间，其最大值，这两个信息是必要的可靠整合任何进化方程。此外，阿夫拉米进化方程肯定会得到改进，特别是，在某种程度上明显地，对于衰落的宗教案例。
英文摘要：
Religious adherence can be considered as a degree of freedom, in a statistical physics sense, for a human agent belonging to a population. The distribution, performance and life time of religions can thus be studied having in mind heterogeneous interacting agent modeling in mind. We present a comprehensive analysis of 58 so called religion (to be better defined in the main text) evolutions, as measured through their number of adherents between 1900 and 2000, - data taken from the World Christian Encyclopedia: 40 are considered to be ''presently growing'' cases, including 11 turn overs in the XX century; 18 are ''presently decaying'', among which 12 are found to have had a recent maximum, in the XIX or the XX century. The Avrami-Kolmogorov differential equation which usually describes solid state transformations, like crystal growth, is used in each case in order to obtain the preferential attachment parameter introduced previously. It is often found close to unity, indicating a smooth evolution. However large values suggest the occurrence of extreme cases which we conjecture are controlled by so called external fields. A few cases indicate the likeliness of a detachment process. We discuss different growing and decaying religions, and illustrate various fits. Some cases seem to indicate the lack of reliability of the data. Others, departure from Avrami law. We point out two difficulties in the analysis : (i) the ''precise'' original time of apparition of a religion, (ii) the time of its maximum, both informations being necessary for integrating reliably any evolution equation. Moreover the Avrami evolution equation might be surely improved, in particular, and somewhat obviously, for the decaying religion cases.
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