In this work we present a general derivation of relativistic fluid dynamics from the Boltzmann equation using the method of moments. The main difference between our approach and the traditional 14-moment approximation is that we will not close the fluid-dynamical equations of motion by truncating the expansion of the distribution function. Instead, we keep all terms in the moment expansion. The reduction of the degrees of freedom is done by identifying the microscopic time scales of the Boltzmann equation and considering only the slowest ones. In addition, the equations of motion for the dissipative quantities are truncated according to a systematic power-counting scheme in Knudsen and inverse Reynolds number. We conclude that the equations of motion can be closed in terms of only 14 dynamical variables, as long as we only keep terms of second order in Knudsen and/or inverse Reynolds number. We show that, even though the equations of motion are closed in terms of these 14 fields, the transport coefficients carry information about all the moments of the distribution function. In this way, we can show that the particle-diffusion and shear-viscosity coefficients agree with the values given by the Chapman-Enskog expansion.

The correct thermodynamic relation has a negative sign that was missing in Eq. (12) and, therefore, n _ dso, h -I > ao 0 € n dSy dn ( 12) In the first line of Eq. (62), the sign of the second term, ((, -Q^Co). was incorrect. This term should have a positive sign and the corrected equation reads m~P i --Q|0 0)n + (£,. -n%JCo)0 = -A-ojn + O(Kn). >(0) -_ o (°) t (62) The remaining two equations listed as part of Eq. (62) have no mistakes. In Eq. (72), the term [the first term on the right-hand side of the second equation listed in Eq. (72)] and the term [the first term on the right-hand side of the third equation listed in Eq. (72)] should be multiplied by t n and x", respectively. The corrected form for Eq. (72) then reads J* = -5nnn^6 -^V^II + ^-X nnnv&lv + XnYiIiF -krmnfwI v,

We investigate the consequences of a nonzero bulk viscosity coefficient on the transverse momentum spectra, azimuthal momentum anisotropy, and multiplicity of charged hadrons produced in heavy ion collisions at LHC energies. The agreement between a realistic 3D hybrid simulation and the experimentally measured data considerably improves with the addition of a bulk viscosity coefficient for strongly interacting matter. This paves the way for an eventual quantitative determination of several QCD transport coefficients from the experimental heavy ion and hadron-nucleus collision programs.

In this work it is shown that the use of a hydrodynamical model of heavy ion collisions which incorporates recent developments, together with updated photon emission rates, greatly improves agreement with both ALICE and PHENIX measurements of direct photons, supporting the idea that thermal photons are the dominant source of direct photon momentum anisotropy. The eventby-event hydrodynamical model uses IP-Glasma initial states and includes, for the first time, both shear and bulk viscosities, along with second order couplings between the two viscosities. The effect of both shear and bulk viscosities on the photon rates is studied, and those transport coefficients are shown to have measurable consequences on the photon momentum anisotropy. arXiv:1509.06738v3 [hep-ph]