Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Constructing higher-order hydrodynamics: The third order   Hydrodynamics can be formulated as the gradient expansion of conserved
currents in terms of the fundamental fields describing the near-equilibrium
fluid flow. In the relativistic case, the Navier-Stokes equations follow from
the conservation of the stress-energy tensor to first order in derivatives. In
this paper, we go beyond the presently understood second-order hydrodynamics
and discuss the systematisation of obtaining the hydrodynamic expansion to an
arbitrarily high order. As an example of the algorithm that we present, we
fully classify the gradient expansion at third order for neutral fluids in four
dimensions, thus finding the most general next-to-leading-order corrections to
the relativistic Navier-Stokes equations in curved space-time. In doing so, we
list $20$ new transport coefficient candidates in the conformal and $68$ in the
non-conformal case. As we do not consider any constraints that could
potentially arise from the local entropy current analysis, this is the maximal
possible set of neutral third-order transport coefficients. To investigate the
physical implications of these new transport coefficients, we obtain the
third-order corrections to the linear dispersion relations that describe the
propagation of diffusion and sound waves in relativistic fluids. We also
compute the corrections to the scalar (spin-$2$) two-point correlation function
of the third-order stress-energy tensor. Furthermore, as an example of a
non-linear hydrodynamic flow, we calculate the third-order corrections to the
energy density of a boost-invariant Bjorken flow. Finally, we apply our field
theoretic results to the $\mathcal{N}=4$ supersymmetric Yang-Mills fluid at
infinite 't Hooft coupling and infinite number of colours to find the values of
five new linear combinations of the conformal transport coefficients.

9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph