Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Second-order Relativistic Hydrodynamic Equations for Viscous Systems;
  how does the dissipation affect the internal energy?   We derive the second-order dissipative relativistic hydrodynamic equations in
a generic frame with a continuous parameter from the relativistic Boltzmann
equation. We present explicitly the relaxation terms in the energy and particle
frames. Our results show that the viscosities are frame-independent but the
relaxation times are generically frame-dependent. We confirm that the
dissipative part of the energy-momentum tensor in the particle frame satisfies
$\delta T^\mu_\mu = 0$ obtained for the first-order equation before, in
contrast to the Eckart choice $u_\mu \delta T^{\mu\nu} u_\nu = 0$ adopted as a
matching condition in the literature. We emphasize that the new constraint
$\delta T^\mu_\mu = 0$ can be compatible with the phenomenological derivation
of hydrodynamics based on the second law of thermodynamics.

33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas