Testing Zipfian and Heaps’ Laws in Classical Chinese: Diachronic Parameter Dynamics and Lexical Diversity Over Two Millennia

Zipf’s law, Zipf-Mandelbrot law and Heaps’ law have been validated across languages and are viewed as universal linguistic principles. Recent studies increasingly investigated their parameter implications. However, their applicability to ancient languages remains underexplored, and the exponent of Heaps’ law has received limited attention. Our study explores how well these laws hold in Classical Chinese and whether their exponents can serve as diachronic indicators of lexical diversity. The results indicate that Classical Chinese exhibits distributional patterns consistent with the laws. The exponent of Zipf’s law decreases diachronically, whereas that of Heaps’ law and lexical diversity increase. The exponent of Zipf’s law correlates negatively with lexical diversity, that of Heaps’ law positively, and all the three show strong pairwise correlations. The parameters of Zipf-Mandelbrot law exhibit no clear monotonic trend and correlate only internally. Our findings provide support for the three laws in Classical Chinese and demonstrate both the exponents of Zipf’s law and Heaps’ law function as diachronic indicators of lexical diversity in Classical Chinese. However, the study is limited by its language scope, metric choice, missing polysemy analysis, untested mechanisms and unit-related issues. Future research could further extend these points.