{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T17:36:56Z","timestamp":1779903416687,"version":"3.53.1"},"reference-count":36,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,9,14]],"date-time":"2025-09-14T00:00:00Z","timestamp":1757808000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This study explores the nonlinear dynamics and interdependencies among major commodity markets\u2014Gold, Oil, Natural Gas, and Silver\u2014by employing advanced chaos theory and information-theoretic tools. Using daily data from 2020 to 2024, we estimate key complexity measures including Lyapunov exponents, correlation dimension, Shannon and R\u00e9nyi entropy, and mutual information. We also apply the stochastic SO(2) Lie group method to model dynamic correlations, and wavelet coherence analysis to detect time-frequency co-movements. Our findings reveal evidence of low-dimensional deterministic chaos and time-varying nonlinear relationships, especially among pairs like Gold\u2013Silver and Oil\u2013Gas. These results highlight the importance of using nontraditional approaches to uncover hidden structure and co-movement dynamics in commodity markets, providing useful insights for portfolio diversification and systemic risk assessment.<\/jats:p>","DOI":"10.3390\/e27090955","type":"journal-article","created":{"date-parts":[[2025,9,16]],"date-time":"2025-09-16T08:56:46Z","timestamp":1758013006000},"page":"955","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Entropy and Chaos-Based Modeling of Nonlinear Dependencies in Commodity Markets"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8536-5636","authenticated-orcid":false,"given":"Irina","family":"Georgescu","sequence":"first","affiliation":[{"name":"Department of Economic Informatics and Cybernetics, Bucharest University of Economics, Calea Doroban\u021bi, 010552 Bucharest, Romania"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0154-6617","authenticated-orcid":false,"given":"Jani","family":"Kinnunen","sequence":"additional","affiliation":[{"name":"School of Business, LUT University, Yliopistonkatu 34, 53851 Lappeenranta, Finland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Muniz, M., Ehrhardt, M., and G\u00fcnther, M. 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