{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:16:14Z","timestamp":1760145374701,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,7,24]],"date-time":"2024-07-24T00:00:00Z","timestamp":1721779200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"STFC in the UK","award":["ST\/V000551\/1","CEX2020-001058-M"],"award-info":[{"award-number":["ST\/V000551\/1","CEX2020-001058-M"]}]},{"name":"Spanish program Unidad de Excelencia Maria de Maeztu","award":["ST\/V000551\/1","CEX2020-001058-M"],"award-info":[{"award-number":["ST\/V000551\/1","CEX2020-001058-M"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We develop an action principle for producing a single-fluid two-constituent system with dissipation in general relativity. The two constituents in the model are particles and entropy. The particle flux creation rate is taken to be zero, while the entropy creation rate is non-zero. Building on previous work, it is demonstrated that a new term (the proper time derivative of the matter space \u201cmetric\u201d) is required in the Lagrangian in order to produce terms typically associated with bulk and shear viscosity. Equations of motion, entropy creation rate, and energy\u2013momentum\u2013stress tensor are derived. Using an Onsager approach of identifying thermodynamic \u201cforces\u201d and \u201cfluxes\u201d, a model is produced which delivers the same entropy creation rate as the standard, relativistic Navier\u2013Stokes equations. This result is then contrasted with a model generated in the spirit of the action principle, which takes as its starting point a specific Lagrangian and then produces the equations of motion, entropy creation rate, and energy\u2013momentum\u2013stress tensor. Unlike the equations derived from Onsager reasoning, where the analogs of the bulk and shear viscosity coefficients are prescribed \u201cexternally\u201d, we find that the forms of the coefficients in the second example are a direct result of the specified Lagrangian. Furthermore, the coefficients are shown to satisfy evolution equations along the fluid worldline, also a product of the specific Lagrangian.<\/jats:p>","DOI":"10.3390\/e26080621","type":"journal-article","created":{"date-parts":[[2024,7,24]],"date-time":"2024-07-24T14:55:47Z","timestamp":1721832947000},"page":"621","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Field-Theory Approach for Modeling Dissipative Relativistic Fluids"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8550-3843","authenticated-orcid":false,"given":"Nils","family":"Andersson","sequence":"first","affiliation":[{"name":"Mathematical Sciences and STAG Research Centre, University of Southampton, Southampton SO17 1BJ, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6515-3644","authenticated-orcid":false,"given":"Thomas","family":"Celora","sequence":"additional","affiliation":[{"name":"Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Magrans, 08193 Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7937-1490","authenticated-orcid":false,"given":"Gregory","family":"Comer","sequence":"additional","affiliation":[{"name":"Department of Physics, Saint Louis University, St. Louis, MO 63156-0907, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4805-0309","authenticated-orcid":false,"given":"Ian","family":"Hawke","sequence":"additional","affiliation":[{"name":"Mathematical Sciences and STAG Research Centre, University of Southampton, Southampton SO17 1BJ, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"161101","DOI":"10.1103\/PhysRevLett.119.161101","article-title":"GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral","volume":"119","author":"Abbott","year":"2017","journal-title":"Phys. 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