{"title":"揭示相对论流体动力学中的非正则哈密顿结构","authors":"Keiichiro Takeda , Naoki Sato","doi":"10.1016/j.fpp.2025.100092","DOIUrl":null,"url":null,"abstract":"<div><div>We present the noncanonical Hamiltonian structure of the relativistic Euler equations for a perfect fluid in Minkowski spacetime. By identifying the system’s noncanonical Poisson bracket and Hamiltonian, we show that relativistic fluid flows preserve helicity and enstrophy as conserved quantities in three-dimensional and two-dimensional cases, respectively. This holds when the fluid follows a relativistic <span><math><mi>γ</mi></math></span>-barotropic equation of state, which generalizes the classical barotropic condition. Furthermore, we demonstrate that these conserved quantities are Casimir invariants associated with the noncanonical Poisson structure. These findings open new avenues for applying Hamiltonian theory to the study of astrophysical fluids and relativistic plasmas.</div></div>","PeriodicalId":100558,"journal":{"name":"Fundamental Plasma Physics","volume":"14 ","pages":"Article 100092"},"PeriodicalIF":0.0000,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Revealing noncanonical Hamiltonian structures in relativistic fluid dynamics\",\"authors\":\"Keiichiro Takeda , Naoki Sato\",\"doi\":\"10.1016/j.fpp.2025.100092\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We present the noncanonical Hamiltonian structure of the relativistic Euler equations for a perfect fluid in Minkowski spacetime. By identifying the system’s noncanonical Poisson bracket and Hamiltonian, we show that relativistic fluid flows preserve helicity and enstrophy as conserved quantities in three-dimensional and two-dimensional cases, respectively. This holds when the fluid follows a relativistic <span><math><mi>γ</mi></math></span>-barotropic equation of state, which generalizes the classical barotropic condition. Furthermore, we demonstrate that these conserved quantities are Casimir invariants associated with the noncanonical Poisson structure. These findings open new avenues for applying Hamiltonian theory to the study of astrophysical fluids and relativistic plasmas.</div></div>\",\"PeriodicalId\":100558,\"journal\":{\"name\":\"Fundamental Plasma Physics\",\"volume\":\"14 \",\"pages\":\"Article 100092\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2025-04-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Fundamental Plasma Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S2772828525000093\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fundamental Plasma Physics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2772828525000093","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Revealing noncanonical Hamiltonian structures in relativistic fluid dynamics
We present the noncanonical Hamiltonian structure of the relativistic Euler equations for a perfect fluid in Minkowski spacetime. By identifying the system’s noncanonical Poisson bracket and Hamiltonian, we show that relativistic fluid flows preserve helicity and enstrophy as conserved quantities in three-dimensional and two-dimensional cases, respectively. This holds when the fluid follows a relativistic -barotropic equation of state, which generalizes the classical barotropic condition. Furthermore, we demonstrate that these conserved quantities are Casimir invariants associated with the noncanonical Poisson structure. These findings open new avenues for applying Hamiltonian theory to the study of astrophysical fluids and relativistic plasmas.