Third-order dissipative hydrodynamics from kinetic theory

Relativistic hydrodynamics has been used to study hot and dense
nuclear matter created in heavy-ion collisions with considerable
success. The theory is formulated as an expansion in gradients of
velocity with ideal hydrodynamics being zeroth-order and non-ideal
effects appearing in higher order theories.  Relativistic
Navier-Stokes theory which is a dissipative first-order theory has
acausal behaviour. This is rectified in the second-order
Israel-Stewart theory. It is thus of interest to formulate a
third-order theory and quantify its differences from existing
theories.

An attempt to derive a third-order theory from entropy consideration
has already been made. However this fails to capture all the terms in
the evolution equations and hence is incomplete. A complete
formulation of third-order viscous hydrodynamics from kinetic theory
will be presented and numerical results for the boost-invariant
Bjorken flow will be discussed.