Relativistic third-order viscous corrections to the entropy four-current from kinetic theory

Abstract

By employing a Chapman-Enskog like iterative solution of the Boltzmann equation in relaxation-time approximation, we derive a new expression for the entropy four-current up to third order in gradient expansion. We show that unlike second-order and third-order entropy four-current obtained using Grad's method, there is a non-vanishing entropy flux in the present third-order expression. We further quantify the effect of the higher-order entropy density in the case of boost-invariant one-dimensional longitudinal expansion of a system. We demonstrate that the results obtained using third-order evolution equation for shear stress tensor, derived by employing the method of Chapman-Enskog expansion, show better agreement with the exact solution of the Boltzmann equation as well as with the parton cascade BAMPS, as compared to those obtained using the third-order equations from the method of Grad's 14-moment approximation.

8 pages, 8 figures, published version

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• Extensivity, entropy current, area law and Unruh effect
• Transasymptotics and hydrodynamization of the Fokker-Planck equation for gluons
• Relativistic dissipation obeys Chapman-Enskog asymptotics: analytical and numerical evidence as a basis for accurate kinetic simulations
• Steady asymptotic equilibria in conformal relativistic fluids
• Non-conformal evolution of magnetic fields during reheating
• Entropy current in relativistic quantum statistical mechanics