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In simulations of high energy heavy ion collisions that employ viscoushydrodynamics, single particle distributions are distorted from their thermalequilibrium form due to gradients in the flow velocity. These are closelyrelated to the formulas for the shear and bulk viscosities in thequasi-particle approximation. Distorted single particle distributions are nowcommonly used to calculate the emission of photons and dilepton pairs, and inthe late stage to calculate the conversion of a continuous fluid to individualparticles. We show how distortions of the single particle distributionfunctions due to both shear and bulk viscous effects can be done rigorously inthe quasi-particle approximation and illustrate it with the linear $\sigma$model at finite temperature.

Departure from Equilibrium of the Quasi-Particle Distribution Functions in High Energy Nuclear Collisions