Measuring information density in interlanguage through entropy analysis.

Interlanguage development is often assessed through structural counts that only partially capture how learner language is organized probabilistically. This study examines whether information-theoretic indicators are sensitive to proficiency-linked distributional differences in argumentative interlanguage writing. It analyzes 200 de-identified argumentative essays: 143 L2 English essays labeled B1, B2, or C1 and 57 genre-matched L1 English essays used as a reference sample. The primary analysis focuses on four operational indicators: lexical entropy (Hlex), grammatical divergence from an L1 reference distribution using POS trigrams (KLgram), compression ratio (CR), and the positional concentration index (PCI). The broader analytical framework also includes an exploratory phraseological layer operationalized as entropy over contiguous 3-word lexical sequences. Descriptive results suggested increasing phraseological dispersion across proficiency levels; however, because more than 90% of these sequences occurred only once within the fixed 250-token windows, the estimates were treated as supplemental and were excluded from the primary inferential analysis. Welch's ANOVA and Games-Howell post hoc tests indicated ordered group differences in the observed analytic sample. Hlex and PCI increased across proficiency groups, whereas KLgram and CR decreased, suggesting broader lexical dispersion, closer local grammatical alignment with the L1 reference distribution, greater global structural regularity, and stronger early information packaging. The findings are interpreted as evidence of probabilistic reorganization within this bounded argumentative-writing corpus, not as a universal model of L2 development or as a mathematical validation of the measures. They should be read in light of the study's genre, sampling, annotation, fixed-window, metadata, and data-sharing constraints.