{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,11,4]],"date-time":"2026-11-04T00:00:03Z","timestamp":1793750403243,"version":"4.6.1"},"reference-count":74,"publisher":"American Physical Society (APS)","issue":"2","license":[{"start":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T00:00:00Z","timestamp":1783382400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100013927","name":"Fondation Merac","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100013927","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004815","name":"Isaac Newton Trust","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004815","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Cambridge Centre for Theoretical Cosmology"}],"content-domain":{"domain":["journals.aps.org"],"crossmark-restriction":true},"short-container-title":["Phys. Rev. Lett."],"accepted":{"date-parts":[[2026,6,11]]},"abstract":"<jats:p>In relativity, relaxation processes are often assumed to undergo time dilation under Lorentz boosts. We show that this intuition fails generically. Because of relativity of simultaneity, Lorentz boosts can split a single relaxation mode into a continuum of excitations, with a width set by the maximal signal propagation speed. Focusing on linearized relativistic (kinetic or rheological) theories with an Onsager-type symmetry, we derive rigorous bounds on relaxation spectra in arbitrary inertial frames, expressed solely in terms of rest-frame spectral data at zero wave number. As a consequence, nonhydrodynamic gaps, maximal relaxation rates, and the convergence radii of hydrodynamic modes obey nontrivial Lorentz-covariant constraints. These results provide a unified framework for understanding how relativity constrains relaxation dynamics in many-body systems.<\/jats:p>","DOI":"10.1103\/d2xr-rj7g","type":"journal-article","created":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T12:33:50Z","timestamp":1781181230000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["How Lorentz Boosts Reshape Relaxation Spectra"],"prefix":"10.1103","volume":"137","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6603-9253","authenticated-orcid":true,"given":"L.","family":"Gavassino","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/013meh722","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Cambridge"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"16","published-online":{"date-parts":[[2026,7,7]]},"reference":[{"key":"d2xr-rj7gCc1R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.72.086009","type":"journal-article"},{"key":"d2xr-rj7gCc2R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.81.114039","type":"journal-article"},{"key":"d2xr-rj7gCc3R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.83.074019","type":"journal-article"},{"key":"d2xr-rj7gCc4R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.113.261601","type":"journal-article"},{"key":"d2xr-rj7gCc5R1","doi-asserted-by":"publisher","DOI":"10.1140\/epjc\/s10052-016-4169-7","type":"journal-article"},{"key":"d2xr-rj7gCc6R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP07(2016)151","type":"journal-article"},{"key":"d2xr-rj7gCc7R1","doi-asserted-by":"publisher","DOI":"10.1140\/epjc\/s10052-019-7271-9","type":"journal-article"},{"key":"d2xr-rj7gCc8R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP05(2018)084","type":"journal-article"},{"key":"d2xr-rj7gCc9R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.122.251601","type":"journal-article"},{"key":"d2xr-rj7gCc10R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP10(2019)034","type":"journal-article"},{"key":"d2xr-rj7gCc11R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.physletb.2022.137202","type":"journal-article"},{"key":"d2xr-rj7gCc12R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.106.056010","type":"journal-article"},{"key":"d2xr-rj7gCc13R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41567-024-02635-5","type":"journal-article"},{"key":"d2xr-rj7gCc14R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.110.116027","type":"journal-article"},{"key":"d2xr-rj7gCc15R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.110.076003","type":"journal-article"},{"key":"d2xr-rj7gCc16R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.6.L042043","type":"journal-article"},{"key":"d2xr-rj7gCc17R1","doi-asserted-by":"publisher","DOI":"10.21468\/SciPostPhys.20.1.020","type":"journal-article"},{"key":"d2xr-rj7gCc18R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP08(2024)065","type":"journal-article"},{"key":"d2xr-rj7gCc19R1","doi-asserted-by":"publisher","DOI":"10.1103\/b8yz-9rj7","type":"journal-article"},{"key":"d2xr-rj7gCc20R1","doi-asserted-by":"publisher","DOI":"10.1103\/v4tj-fj5k","type":"journal-article"},{"key":"d2xr-rj7gCc21R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.31.725","type":"journal-article"},{"key":"d2xr-rj7gCc22R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.12.041001","type":"journal-article"},{"key":"d2xr-rj7gCc23R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP05(2026)215","type":"journal-article"},{"key":"d2xr-rj7gCc25R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.physletb.2023.137854","type":"journal-article"},{"key":"d2xr-rj7gCc26R1","unstructured":"For clarity, we work at finite D, which in kinetic theory amounts to truncating the moment expansion at some very large number (e.g., 10100 moments). This is physically acceptable: the distribution function is already a coarse-grained object, and kinetic theory ceases to hold at too fine momentum resolution (Ref.\u00a0[27], Sec.\u00a03.1).","type":"other"},{"key":"d2xr-rj7gCc27R1","volume-title":"Statistical Mechanics","author":"K. Huang","year":"1987","type":"book"},{"key":"d2xr-rj7gCc28R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.128.010606","type":"journal-article"},{"key":"d2xr-rj7gCc29R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.128.010606","type":"journal-article"},{"key":"d2xr-rj7gCc30R1","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4916(91)90063-E","type":"journal-article"},{"key":"d2xr-rj7gCc31R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.107.065013","type":"journal-article"},{"key":"d2xr-rj7gCc32R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.132.222302","type":"journal-article"},{"key":"d2xr-rj7gCc33R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.110.016020","type":"journal-article"},{"key":"d2xr-rj7gCc34R1","doi-asserted-by":"publisher","DOI":"10.3390\/sym12091543","type":"journal-article"},{"key":"d2xr-rj7gCc35R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.111.103011","type":"journal-article"},{"key":"d2xr-rj7gCc36R1","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4916(79)90130-1","type":"journal-article"},{"key":"d2xr-rj7gCc37R1","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4916(83)90288-9","type":"journal-article"},{"key":"d2xr-rj7gCc38R1","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4916(90)90366-V","type":"journal-article"},{"key":"d2xr-rj7gCc39R1","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4916(86)90164-8","type":"journal-article"},{"key":"d2xr-rj7gCc40R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.99.013105","type":"journal-article"},{"key":"d2xr-rj7gCc41R1","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6382\/acc165","type":"journal-article"},{"key":"d2xr-rj7gCc42R1","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1991.0034","type":"journal-article"},{"key":"d2xr-rj7gCc43R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.43.1223","type":"journal-article"},{"key":"d2xr-rj7gCc44R1","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6382\/ac79f4","type":"journal-article"},{"key":"d2xr-rj7gCc45R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.109.096041","type":"journal-article"},{"key":"d2xr-rj7gCc46R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.37.405","type":"journal-article"},{"key":"d2xr-rj7gCc47R1","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.17.343","type":"journal-article"},{"key":"d2xr-rj7gCc48R1","doi-asserted-by":"publisher","DOI":"10.1063\/1.860614","type":"journal-article"},{"key":"d2xr-rj7gCc49R1","unstructured":"See Supplemental Material at http:\/\/link.aps.org\/supplemental\/10.1103\/d2xr-rj7g for some explicit proofs and examples that were omitted from the main text.","type":"other"},{"key":"d2xr-rj7gCc50R1","doi-asserted-by":"publisher","DOI":"10.1063\/1.530958","type":"journal-article"},{"key":"d2xr-rj7gCc51R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.99.086012","type":"journal-article"},{"key":"d2xr-rj7gCc52R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.98.036006","type":"journal-article"},{"key":"d2xr-rj7gCc53R1","volume-title":"Theory of Elasticity","author":"L.\u2009D. Landau","year":"1986","type":"book"},{"key":"d2xr-rj7gCc54R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.100.106014","type":"journal-article"},{"key":"d2xr-rj7gCc55R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2020.04.002","type":"journal-article"},{"key":"d2xr-rj7gCc56R1","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6382\/ace587","type":"journal-article"},{"key":"d2xr-rj7gCc57R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.109.096040","type":"journal-article"},{"key":"d2xr-rj7gCc58R1","doi-asserted-by":"publisher","DOI":"10.1103\/3kx1-156x","type":"journal-article"},{"key":"d2xr-rj7gCc59R1","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-37276-6","type":"book","volume-title":"Special Relativity in General Frames: From Particles to Astrophysics","author":"E. Gourgoulhon","year":"2013"},{"key":"d2xr-rj7gCc60R1","doi-asserted-by":"crossref","unstructured":"C. Cercignani and G.\u2009M. Kremer, The relativistic Boltzmann equation: Theory and applications (Birkh\u00e4user Verlag, Basel, Boston, Berlin, 2002).","DOI":"10.1007\/978-3-0348-8165-4","type":"other"},{"key":"d2xr-rj7gCc61R1","unstructured":"In kinetic theory, one usually finds that, for each k&gt;0, there is a continuum of \u201cimproper\u201d solutions of (4), with |Re\u03c9| extending up to k, but never beyond [5].","type":"other"},{"key":"d2xr-rj7gCc62R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.132.162301","type":"journal-article"},{"key":"d2xr-rj7gCc63R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.130.261601","type":"journal-article"},{"key":"d2xr-rj7gCc64R1","unstructured":"For any invertible D\u00d7D matrix S, we can write E\u03bc=S\u2020E\u02dc\u03bcS and \u03c3=S\u2020\u03c3\u02dcS, where E\u02dc\u03bc and \u03c3\u02dc are Hermitian and inherit the positivity properties of the originals. Plugging these decompositions into (3), we obtain an equivalent theory E\u02dc\u03bc\u2202\u03bc\u03a8\u02dc=\u2212\u03c3\u02dc\u03a8\u02dc, with \u03a8\u02dc=S\u03a8.","type":"other"},{"key":"d2xr-rj7gCc65R1","volume-title":"Mathematical Methods in Quantum Mechanics with Applications to Schr\u00f6dinger Operators","author":"G. Teschl","year":"2009","type":"book"},{"key":"d2xr-rj7gCc66R1","doi-asserted-by":"crossref","DOI":"10.1007\/978-93-86279-45-3","type":"book","volume-title":"Notes on Functional Analysis","author":"R. Bhatia","year":"2009"},{"key":"d2xr-rj7gCc67R1","volume-title":"Comptes rendus hebdomadaires des s\u00e9ances de l\u2019Acad\u00e9mie des sciences","author":"C. Cattaneo","year":"1958","type":"book"},{"key":"d2xr-rj7gCc68R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.110.094012","type":"journal-article"},{"key":"d2xr-rj7gCc69R1","doi-asserted-by":"publisher","DOI":"10.21468\/SciPostPhys.11.3.054","type":"journal-article"},{"key":"d2xr-rj7gCc70R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevC.110.044903","type":"journal-article"},{"key":"d2xr-rj7gCc71R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevC.111.064910","type":"journal-article"},{"key":"d2xr-rj7gCc72R1","unstructured":"Density-frame hydrodynamics posits that, in any inertial frame (not necessarily comoving), the conserved fluxes JIk admit an expansion in powers of spatial derivatives of the conserved densities JI0. Equivalently, that the hydrodynamic eigenfrequencies \u03c9 can be expanded in powers of the spatial wave vector kj.","type":"other"},{"key":"d2xr-rj7gCc73R1","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-66282-9","type":"book","volume-title":"Perturbation Theory for Linear Operators","author":"T. Kato","year":"1995"},{"key":"d2xr-rj7gCc74R1","doi-asserted-by":"publisher","DOI":"10.1143\/ptp\/4.4.514","type":"journal-article"},{"key":"d2xr-rj7gCc75R1","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6382\/abe588","type":"journal-article"}],"container-title":["Physical Review Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.aps.org\/article\/10.1103\/d2xr-rj7g","content-type":"unspecified","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/harvest.aps.org\/v2\/journals\/articles\/10.1103\/d2xr-rj7g\/fulltext","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T18:01:33Z","timestamp":1790877693000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.aps.org\/doi\/10.1103\/d2xr-rj7g"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7,7]]},"references-count":74,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,7]]}},"URL":"https:\/\/doi.org\/10.1103\/d2xr-rj7g","relation":{"has-preprint":[{"id-type":"doi","id":"10.48550\/arXiv.2601.03081","asserted-by":"subject"}]},"ISSN":["0031-9007","1079-7114"],"issn-type":[{"value":"0031-9007","type":"print"},{"value":"1079-7114","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7,7]]},"assertion":[{"value":"2026-01-19","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"Published by the American Physical Society. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright_statement","label":"Copyright statement","group":{"name":"copyright","label":"copyright"}},{"value":"2026","name":"copyright_year","label":"Copyright year","group":{"name":"copyright","label":"copyright"}},{"value":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/","name":"creative_commons_license","label":"Creative Commons license","group":{"name":"licenses","label":"Licenses"}},{"value":"\u00a92026 The authors","name":"copyright_holder","label":"Copyright holder","group":{"name":"copyright","label":"copyright"}}],"article-number":"022301"}}