We analyze the occurrence frequencies of over 15 million words recorded in
millions of books published during the past two centuries in seven different
languages. For all languages and chronological subsets of the data we confirm
that two scaling regimes characterize the word frequency distributions, with
only the more common words obeying the classic Zipf law. Using corpora of
unprecedented size, we test the allometric scaling relation between the corpus
size and the vocabulary size of growing languages to demonstrate a decreasing
marginal need for new words, a feature that is likely related to the underlying
correlations between words. We calculate the annual growth fluctuations of word
use which has a decreasing trend as the corpus size increases, indicating a
slowdown in linguistic evolution following language expansion. This "cooling
pattern" forms the basis of a third statistical regularity, which unlike the
Zipf and the Heaps law, is dynamical in nature.

本研究对过去两个世纪出版的几百万本书的 15 亿余个单词进行了分析，发现单词使用频率的分布有两个不同的尺度，且随着语料库的增大，新词的需求呈减少趋势，这种 ' 冷却模式 ' 成为第三个动态的统计规律。

语言的增长降低了对新词的需求：一种异速生长的解释

Languages cool as they expand: Allometric scaling and the decreasing  need for new words

We unveil collective effects induced by imitation and social pressure by
analyzing data from three different sources: birth rates, sales of cell phones
and the drop of applause in concert halls. We interpret our results within the
framework of the Random Field Ising Model, which is a threshold model for
collective decisions accounting both for agent heterogeneity and social
imitation. Changes of opinion can occur either abruptly or continuously,
depending on the importance of herding effects. The main prediction of the
model is a scaling relation between the height h of the speed of variation peak
and its width $w$ of the form h ~ w^{-kappa}, with kappa = 2/3 for well
connected populations. Our three sets of data are compatible with such a
prediction, with kappa ~ 0.62 for birth rates, kappa ~ 0.71 for cell phones and
kappa ~ 0.64 for clapping. In this last case, we in fact observe that some
clapping samples end discontinuously (w=0), as predicted by the model for
strong enough imitation.

通过分析出生率、手机销售和音乐会掌声降低等数据集，运用随机场伊辛模型，研究了模仿和社会压力带来的群体效应，发现其具有标度关系 h ~ w^{-kappa}，其中 kappa 取 0.62~0.71。