Relativistic third-order dissipative fluid dynamics from kinetic theory

Abstract

We present the derivation of a novel third-order hydrodynamic evolution equation for shear stress tensor from kinetic theory. Boltzmann equation with relaxation time approximation for the collision term is solved iteratively using Chapman-Enskog like expansion to obtain the nonequilibrium phase-space distribution function. Subsequently, the evolution equation for shear stress tensor is derived from its kinetic definition up-to third-order in gradients. We quantify the significance of the new derivation within one-dimensional scaling expansion and demonstrate that the results obtained using third-order viscous equations derived here provides a very good approximation to the exact solution of Boltzmann equation in relaxation time approximation. We also show that the time evolution of pressure anisotropy obtained using our equations is in better agreement with transport results when compared with an existing third-order calculation based on the second-law of thermodynamics.

6 pages, 3 figures, version to appear in PRC (Rapid Comm)

References in corpus (6)

• Dissipative relativistic fluid dynamics: a new way to derive the equations of motion from kinetic theory
• Relativistic dissipative hydrodynamics from kinetic theory with relaxation time approximation
• The applicability of causal dissipative hydrodynamics to relativistic heavy ion collisions
• Transport rates and momentum isotropization of gluon matter in ultrarelativistic heavy-ion collisions
• Constraining relativistic viscous hydrodynamical evolution
• Thermalization of a color glass condensate and review of the "Bottom-Up" scenario

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