{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:34:18Z","timestamp":1760060058026,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,8,1]],"date-time":"2025-08-01T00:00:00Z","timestamp":1754006400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We establish a rigorous kinetic-theoretical framework to analyze causal propagation in thermal transport phenomena within relativistic ideal fluids, building a more rigorous framework based on the kinetic theory of gases. Specifically, we provide a refined derivation of the wave equation governing thermal and density fluctuations, clarifying its hyperbolic nature and the associated characteristic propagation speeds. The analysis confirms that thermal fluctuations in a simple non-degenerate relativistic fluid satisfy a causal wave equation in the Euler regime, and it recovers the classical expression for the speed of sound in the non-relativistic limit. This work offers enhanced mathematical and physical insights, reinforcing the validity of the hyperbolic description and suggesting a foundation for future studies in dissipative relativistic hydrodynamics.<\/jats:p>","DOI":"10.3390\/axioms14080598","type":"journal-article","created":{"date-parts":[[2025,8,5]],"date-time":"2025-08-05T08:46:55Z","timestamp":1754383615000},"page":"598","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Mathematical Formulation of Causal Propagation in Relativistic Ideal Fluids"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3351-510X","authenticated-orcid":false,"given":"Dominique","family":"Brun-Battistini","sequence":"first","affiliation":[{"name":"Departamento de F\u00edsica y Matem\u00e1ticas, Universidad Iberoamericana, Mexico City C.P. 01219, Mexico"}]},{"given":"Alfredo","family":"Sandoval-Villalbazo","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica y Matem\u00e1ticas, Universidad Iberoamericana, Mexico City C.P. 01219, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9674-2118","authenticated-orcid":false,"given":"Hernando Efrain","family":"Caicedo-Ortiz","sequence":"additional","affiliation":[{"name":"Direcci\u00f3n de Investigaci\u00f3n y Posgrado, Universidad Nacional Rosario Castellanos, Mexico City C.P. 07969, Mexico"},{"name":"Preparatoria \u00c1lvaro Obreg\u00f3n II, Vasco de Quiroga, Instituto de Educaci\u00f3n Media Superior de la Ciudad de M\u00e9xico, Mexico City C.P. 01740, Mexico"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"428","DOI":"10.1016\/S0378-4371(99)00607-X","article-title":"The relativistic kinetic formalism revisited","volume":"278","year":"2000","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1103\/PhysRev.58.267","article-title":"The Thermodynamics of Irreversible Processes. III. Relativistic Theory of the Simple Fluid","volume":"58","author":"Eckart","year":"1940","journal-title":"Phys. Rev."},{"key":"ref_3","unstructured":"Landau, L., and Lifshitz, E.M. (1958). Fluid Mechanics, Addison Wesley."},{"key":"ref_4","unstructured":"de Groot, S.R., van Leeuwen, W.A., and van der Weert, C. (1980). Relativistic Kinetic Theory, North Holland Publ. Co."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"115102","DOI":"10.1088\/0954-3899\/35\/11\/115102","article-title":"Stability and causality in relativistic dissipative hydrodynamics","volume":"35","author":"Denicol","year":"2008","journal-title":"J. Phys. 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