more notes on viscous hydro

references.bib

@@ -685,6 +685,34 @@
   year = "2022"
 }
 
+@article{Banerjee:2012iz,
+  author = "Banerjee, Nabamita and Bhattacharya, Jyotirmoy and Bhattacharyya, Sayantani and Jain, Sachin and Minwalla, Shiraz and Sharma, Tarun",
+  title = "{Constraints on Fluid Dynamics from Equilibrium Partition Functions}",
+  eprint = "1203.3544",
+  archivePrefix = "arXiv",
+  primaryClass = "hep-th",
+  reportNumber = "TFR-TH-12-05, IPMU12-0037",
+  doi = "10.1007/JHEP09(2012)046",
+  journal = "JHEP",
+  volume = "09",
+  pages = "046",
+  year = "2012"
+}
+
+@article{Jensen:2012jh,
+  author = "Jensen, Kristan and Kaminski, Matthias and Kovtun, Pavel and Meyer, Rene and Ritz, Adam and Yarom, Amos",
+  title = "{Towards hydrodynamics without an entropy current}",
+  eprint = "1203.3556",
+  archivePrefix = "arXiv",
+  primaryClass = "hep-th",
+  reportNumber = "CCTP-2012-03",
+  doi = "10.1103/PhysRevLett.109.101601",
+  journal = "Phys. Rev. Lett.",
+  volume = "109",
+  pages = "101601",
+  year = "2012"
+}
+
 %% End BDNK literature
 
 @article{freistuhler2017godunov,

tex/grhd.tex

@@ -4209,6 +4209,42 @@ with gravity}
 
 
 
+\paragraph{\cite{kovtun2019first}: First-Order relativistic hydrodynamics is stable}
+
+\begin{itemize}
+  \item Intro: \question{In a foot note on the first page he mentions that in a relativistic
+    hydro theory the energy density and $U(1)$ carge density are not Lorentz scalars. Why?}
+    The intro repeats the derivation of constitutive relations already presented
+    in \cite{kovtun2012lecture}.
+    He then talks about consequences of extensivity, which IIUC implies further relations
+    among the transport coefficients that ensure thermodynamic consistency.
+    Extensivity is defined in equlibrium and describes
+    locality on length scales that are longer than the equilibrium correlation length.
+    A more detailed discussion about this is given in the refs \cite{Banerjee:2012iz,Jensen:2012jh}.
+  \item Stability of equilibrium: This appears to be a standard analysis of linear perturbations
+    around thermal equilibrium with a plane wave ansatz and then check if there are any growing
+    modes.
+  \item Entropy current: He gives a derivation of that in the appendix. This is done
+    with a general frame. The crucial part in the analysis is that demanding positvity
+    of entropy production while also including higher order derivative corrections gives
+    too restrictive conditions for the transport coefficients. Making it only consistent
+    with first order derivatives then gives a more (apparently?) appealing constraints.
+\end{itemize}
+
+
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 \subsection{Literature review artificial viscosity methods}