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The ideal relativistic rotating gas as a perfect fluid with spin
We show that the ideal relativistic spinning gas at complete thermodynamical equilibrium is a fluid with a non-vanishing spin density tensor σ μν . After having obtained the expression of the local spin-dependent phase-space density f( x, p) στ in the Boltzmann approximation, we derive the spin dens...
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| Published in: | Annals of physics 2010-08, Vol.325 (8), p.1566-1594 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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| cited_by | cdi_FETCH-LOGICAL-c395t-bc86d86690fe7a2709767152f2f561de1133a9011f800a4fc197112aee3c95933 |
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| cites | cdi_FETCH-LOGICAL-c395t-bc86d86690fe7a2709767152f2f561de1133a9011f800a4fc197112aee3c95933 |
| container_end_page | 1594 |
| container_issue | 8 |
| container_start_page | 1566 |
| container_title | Annals of physics |
| container_volume | 325 |
| creator | Becattini, F. Tinti, L. |
| description | We show that the ideal relativistic spinning gas at complete thermodynamical equilibrium is a fluid with a non-vanishing spin density tensor
σ
μν
. After having obtained the expression of the local spin-dependent phase-space density
f(
x,
p)
στ
in the Boltzmann approximation, we derive the spin density tensor and show that it is proportional to the acceleration tensor Ω
μν
constructed with the Frenet–Serret tetrad. We recover the proper generalization of the fundamental thermodynamical relation, involving an additional term −(1/2)Ω
μν
σ
μν
. We also show that the spin density tensor has a non-vanishing projection onto the four-velocity field, i.e.
t
μ
=
σ
μν
u
ν
≠
0, in contrast to the common assumption
t
μ
=
0, known as Frenkel condition, in the thus-far proposed theories of relativistic fluids with spin. We briefly address the viewpoint of the accelerated observer and inertial spin effects. |
| doi_str_mv | 10.1016/j.aop.2010.03.007 |
| format | article |
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σ
μν
. After having obtained the expression of the local spin-dependent phase-space density
f(
x,
p)
στ
in the Boltzmann approximation, we derive the spin density tensor and show that it is proportional to the acceleration tensor Ω
μν
constructed with the Frenet–Serret tetrad. We recover the proper generalization of the fundamental thermodynamical relation, involving an additional term −(1/2)Ω
μν
σ
μν
. We also show that the spin density tensor has a non-vanishing projection onto the four-velocity field, i.e.
t
μ
=
σ
μν
u
ν
≠
0, in contrast to the common assumption
t
μ
=
0, known as Frenkel condition, in the thus-far proposed theories of relativistic fluids with spin. We briefly address the viewpoint of the accelerated observer and inertial spin effects.</description><identifier>ISSN: 0003-4916</identifier><identifier>EISSN: 1096-035X</identifier><identifier>DOI: 10.1016/j.aop.2010.03.007</identifier><identifier>CODEN: APNYA6</identifier><language>eng</language><publisher>New York: Elsevier Inc</publisher><subject>ACCELERATION ; ANGULAR MOMENTUM ; BOLTZMANN STATISTICS ; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS ; DENSITY ; ENERGY RANGE ; EQUILIBRIUM ; Fluid dynamics ; FLUID FLOW ; FLUIDS ; Gases ; IDEAL FLOW ; INCOMPRESSIBLE FLOW ; MATHEMATICAL SPACE ; PARTICLE PROPERTIES ; PHASE SPACE ; PHYSICAL PROPERTIES ; Relativistic fluids with spin ; RELATIVISTIC RANGE ; Relativistic thermodynamics ; Rotating relativistic gas ; SPACE ; SPIN ; STEADY FLOW ; TENSORS ; Theory ; THERMODYNAMICS ; VELOCITY</subject><ispartof>Annals of physics, 2010-08, Vol.325 (8), p.1566-1594</ispartof><rights>2010 Elsevier Inc.</rights><rights>Copyright © 2010 Elsevier B.V. All rights reserved.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c395t-bc86d86690fe7a2709767152f2f561de1133a9011f800a4fc197112aee3c95933</citedby><cites>FETCH-LOGICAL-c395t-bc86d86690fe7a2709767152f2f561de1133a9011f800a4fc197112aee3c95933</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,780,784,885,27924,27925</link.rule.ids><backlink>$$Uhttps://www.osti.gov/biblio/21457141$$D View this record in Osti.gov$$Hfree_for_read</backlink></links><search><creatorcontrib>Becattini, F.</creatorcontrib><creatorcontrib>Tinti, L.</creatorcontrib><title>The ideal relativistic rotating gas as a perfect fluid with spin</title><title>Annals of physics</title><description>We show that the ideal relativistic spinning gas at complete thermodynamical equilibrium is a fluid with a non-vanishing spin density tensor
σ
μν
. After having obtained the expression of the local spin-dependent phase-space density
f(
x,
p)
στ
in the Boltzmann approximation, we derive the spin density tensor and show that it is proportional to the acceleration tensor Ω
μν
constructed with the Frenet–Serret tetrad. We recover the proper generalization of the fundamental thermodynamical relation, involving an additional term −(1/2)Ω
μν
σ
μν
. We also show that the spin density tensor has a non-vanishing projection onto the four-velocity field, i.e.
t
μ
=
σ
μν
u
ν
≠
0, in contrast to the common assumption
t
μ
=
0, known as Frenkel condition, in the thus-far proposed theories of relativistic fluids with spin. We briefly address the viewpoint of the accelerated observer and inertial spin effects.</description><subject>ACCELERATION</subject><subject>ANGULAR MOMENTUM</subject><subject>BOLTZMANN STATISTICS</subject><subject>CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS</subject><subject>DENSITY</subject><subject>ENERGY RANGE</subject><subject>EQUILIBRIUM</subject><subject>Fluid dynamics</subject><subject>FLUID FLOW</subject><subject>FLUIDS</subject><subject>Gases</subject><subject>IDEAL FLOW</subject><subject>INCOMPRESSIBLE FLOW</subject><subject>MATHEMATICAL SPACE</subject><subject>PARTICLE PROPERTIES</subject><subject>PHASE SPACE</subject><subject>PHYSICAL PROPERTIES</subject><subject>Relativistic fluids with spin</subject><subject>RELATIVISTIC RANGE</subject><subject>Relativistic thermodynamics</subject><subject>Rotating relativistic gas</subject><subject>SPACE</subject><subject>SPIN</subject><subject>STEADY FLOW</subject><subject>TENSORS</subject><subject>Theory</subject><subject>THERMODYNAMICS</subject><subject>VELOCITY</subject><issn>0003-4916</issn><issn>1096-035X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><recordid>eNp9kM1LxDAQxYMouH78Ad6CnrvONJumwYsifsGClxW8hZhO3CxrW5Ou4n9vSj0LA8PAe8PvPcbOEOYIWF1u5rbr5yXkG8QcQO2xGYKuChDydZ_NAEAUC43VITtKaQOAuJD1jF2v1sRDQ3bLI23tEL5CGoLjsRvy0b7zd5v4OLyn6MkN3G93oeHfYVjz1If2hB14u010-reP2cv93er2sVg-Pzzd3iwLJ7QcijdXV01dVRo8KVsq0KpSKEtfellhQ4hCWJ2pfA1gF96hVoilJRJOSy3EMbuY_naZzyQXBnJr17VtZjJlDqNwgVl1Pqn62H3uKA1m0-1im8GMKgXWUkmZRTiJXOxSiuRNH8OHjT8GwYxtmo3JbZqxTQPC5Daz52ryUM74FSiOCNQ6akIcCZou_OP-Baqhelg</recordid><startdate>20100801</startdate><enddate>20100801</enddate><creator>Becattini, F.</creator><creator>Tinti, L.</creator><general>Elsevier Inc</general><general>Elsevier BV</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7U5</scope><scope>8FD</scope><scope>L7M</scope><scope>OTOTI</scope></search><sort><creationdate>20100801</creationdate><title>The ideal relativistic rotating gas as a perfect fluid with spin</title><author>Becattini, F. ; Tinti, L.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c395t-bc86d86690fe7a2709767152f2f561de1133a9011f800a4fc197112aee3c95933</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>ACCELERATION</topic><topic>ANGULAR MOMENTUM</topic><topic>BOLTZMANN STATISTICS</topic><topic>CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS</topic><topic>DENSITY</topic><topic>ENERGY RANGE</topic><topic>EQUILIBRIUM</topic><topic>Fluid dynamics</topic><topic>FLUID FLOW</topic><topic>FLUIDS</topic><topic>Gases</topic><topic>IDEAL FLOW</topic><topic>INCOMPRESSIBLE FLOW</topic><topic>MATHEMATICAL SPACE</topic><topic>PARTICLE PROPERTIES</topic><topic>PHASE SPACE</topic><topic>PHYSICAL PROPERTIES</topic><topic>Relativistic fluids with spin</topic><topic>RELATIVISTIC RANGE</topic><topic>Relativistic thermodynamics</topic><topic>Rotating relativistic gas</topic><topic>SPACE</topic><topic>SPIN</topic><topic>STEADY FLOW</topic><topic>TENSORS</topic><topic>Theory</topic><topic>THERMODYNAMICS</topic><topic>VELOCITY</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Becattini, F.</creatorcontrib><creatorcontrib>Tinti, L.</creatorcontrib><collection>CrossRef</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>OSTI.GOV</collection><jtitle>Annals of physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Becattini, F.</au><au>Tinti, L.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The ideal relativistic rotating gas as a perfect fluid with spin</atitle><jtitle>Annals of physics</jtitle><date>2010-08-01</date><risdate>2010</risdate><volume>325</volume><issue>8</issue><spage>1566</spage><epage>1594</epage><pages>1566-1594</pages><issn>0003-4916</issn><eissn>1096-035X</eissn><coden>APNYA6</coden><abstract>We show that the ideal relativistic spinning gas at complete thermodynamical equilibrium is a fluid with a non-vanishing spin density tensor
σ
μν
. After having obtained the expression of the local spin-dependent phase-space density
f(
x,
p)
στ
in the Boltzmann approximation, we derive the spin density tensor and show that it is proportional to the acceleration tensor Ω
μν
constructed with the Frenet–Serret tetrad. We recover the proper generalization of the fundamental thermodynamical relation, involving an additional term −(1/2)Ω
μν
σ
μν
. We also show that the spin density tensor has a non-vanishing projection onto the four-velocity field, i.e.
t
μ
=
σ
μν
u
ν
≠
0, in contrast to the common assumption
t
μ
=
0, known as Frenkel condition, in the thus-far proposed theories of relativistic fluids with spin. We briefly address the viewpoint of the accelerated observer and inertial spin effects.</abstract><cop>New York</cop><pub>Elsevier Inc</pub><doi>10.1016/j.aop.2010.03.007</doi><tpages>29</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Annals of physics, 2010-08, Vol.325 (8), p.1566-1594 |
| issn | 0003-4916 1096-035X |
| language | eng |
| recordid | cdi_osti_scitechconnect_21457141 |
| source | Elsevier |
| subjects | ACCELERATION ANGULAR MOMENTUM BOLTZMANN STATISTICS CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS DENSITY ENERGY RANGE EQUILIBRIUM Fluid dynamics FLUID FLOW FLUIDS Gases IDEAL FLOW INCOMPRESSIBLE FLOW MATHEMATICAL SPACE PARTICLE PROPERTIES PHASE SPACE PHYSICAL PROPERTIES Relativistic fluids with spin RELATIVISTIC RANGE Relativistic thermodynamics Rotating relativistic gas SPACE SPIN STEADY FLOW TENSORS Theory THERMODYNAMICS VELOCITY |
| title | The ideal relativistic rotating gas as a perfect fluid with spin |
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