Quantitative characterization of complexity of chromatographic profiles using structure-weighted information entropy

Quantitative evaluation of chromatographic separation performance is crucial for method optimization in complex systems. The existing measurement indicators of information entropy use the intensity distribution alone without accounting for the time-domain structure and separation state of chromatographic peaks, which limits their discriminatory power in multi-factor condition optimization. In this study, structure-weighted spatial Rényi entropy (SSRE) was therefore proposed through incorporating a Gaussian structural weighting function and a uniformity correction term accounting for peak spacing, resolution, and response distribution. In 64 full-factorial simulated conditions, the average single-factor sensitivity of SSRE was 36.5%, 2.6 times that of Shannon entropy, while the chromatographic discrimination index (CDI) averaged 1.7 times that of the four classical entropies over 100 repeated runs. SSRE identified the theoretically optimal condition in every run and the classical measures in no more than 26%. The design is also the one used to optimize the SSRE parameters. On a held-out simulation with a different peak model, noise structure and design geometry, the same parameters were applied without refitting and SSRE remained closest to an independent reference with a mean Spearman coefficient of 0.571 against 0.549 for Shannon entropy. In 16 gas chromatography-mass spectrometry (GC-MS) datasets from Lycium barbarum L. (goji), the condition ranked highest by SSRE was among those with the most favourable peak-level parameters. For profiles acquired from the same material system under different pretreatment or acquisition conditions, SSRE provides a peak-detection-free basis for ranking candidate conditions. These findings support SSRE as a complementary measure of chromatographic structure for pretreatment evaluation and method optimization, although broader applicability requires further validation.