Editing Four-vector (section)

==Thermodynamics==

{{see also|Relativistic heat conduction}}

===Four-heat flux===

The four-heat flux vector field, is essentially similar to the 3d [[heat flux]] vector field '''q''', in the local frame of the fluid:<ref>{{Cite journal |first1=Y. M. |last1=Ali |first2=L. C. |last2=Zhang |title=Relativistic heat conduction |journal=Int. J. Heat Mass Trans. |volume=48 |year=2005 |issue=12 |pages=2397–2406 |doi=10.1016/j.ijheatmasstransfer.2005.02.003 }}</ref>

<math display="block">\mathbf{Q} = -k \boldsymbol{\partial} T = -k\left( \frac{1}{c}\frac{\partial T}{\partial t}, \nabla T\right) </math>

where ''T'' is [[absolute temperature]] and ''k'' is [[thermal conductivity]].

===Four-baryon number flux===

The flux of baryons is:<ref>{{Cite book|title=Gravitation|url=https://archive.org/details/gravitation00misn_003|url-access=limited | author1=J.A. Wheeler |author2=C. Misner |author3=K.S. Thorne |publisher=W.H. Freeman & Co|year=1973|pages=[https://archive.org/details/gravitation00misn_003/page/n582 558]–559|isbn=0-7167-0344-0}}</ref>
<math display="block">\mathbf{S} = n\mathbf{U}</math>
where {{math|''n''}} is the [[number density]] of [[baryon]]s in the local [[rest frame]] of the baryon fluid (positive values for baryons, negative for [[antiparticle|anti]]baryons), and {{math|'''U'''}} the [[four-velocity]] field (of the fluid) as above.

===Four-entropy===

The four-[[entropy]] vector is defined by:<ref>{{Cite book|title=Gravitation|url=https://archive.org/details/gravitation00misn_003| url-access=limited|author1=J.A. Wheeler |author2=C. Misner |author3=K.S. Thorne |publisher=W.H. Freeman & Co| year=1973| page=[https://archive.org/details/gravitation00misn_003/page/n591 567]|isbn=0-7167-0344-0}}</ref>
<math display="block">\mathbf{s} = s\mathbf{S} + \frac{\mathbf{Q}}{T}</math>
where {{math|''s''}} is the entropy per baryon, and {{mvar|T}} the [[absolute temperature]], in the local rest frame of the fluid.<ref>{{Cite book|title=Gravitation|url=https://archive.org/details/gravitation00misn_003|url-access=limited|author1=J.A. Wheeler |author2=C. Misner |author3=K.S. Thorne |publisher=W.H. Freeman & Co|year=1973|page=[https://archive.org/details/gravitation00misn_003/page/n582 558]|isbn=0-7167-0344-0}}</ref>