  Relativistic hydrodynamics simulations of quark-gluon plasma play a pivotal
role in our understanding of heavy ion collisions at RHIC and LHC. They are
based on a phenomenological description due to Mueller, Israel, Stewart (MIS)
and others, which incorporates viscous effects and ensures a well-posed initial
value problem. Focusing on the case of conformal plasma we propose a
generalization which includes, in addition, the dynamics of the least damped
far-from-equilibrium degree of freedom found in strongly coupled plasmas
through the AdS/CFT correspondence. We formulate new evolution equations for
general flows and then test them in the case of N=4 super Yang-Mills plasma by
comparing their solutions alongside solutions of MIS theory with numerical
computations of isotropization and boost-invariant flow based on holography. In
these tests the new equations reproduce the results of MIS theory when
initialized close to the hydrodynamic stage of evolution, but give a more
accurate description of the dynamics when initial conditions are set in the
pre-equilibrium regime.
