  In simulations of high energy heavy ion collisions that employ viscous
hydrodynamics, single particle distributions are distorted from their thermal
equilibrium form due to gradients in the flow velocity. These are closely
related to the formulas for the shear and bulk viscosities in the
quasi-particle approximation. Distorted single particle distributions are now
commonly used to calculate the emission of photons and dilepton pairs, and in
the late stage to calculate the conversion of a continuous fluid to individual
particles. We show how distortions of the single particle distribution
functions due to both shear and bulk viscous effects can be done rigorously in
the quasi-particle approximation and illustrate it with the linear $\sigma$
model at finite temperature.
