  We present a new variational framework for dissipative general relativistic
fluid dynamics. The model extends the convective variational principle for
multi-fluid systems to account for a range of dissipation channels. The key
ingredients in the construction are i) the use of a lower dimensional matter
space for each fluid component, and ii) an extended functional dependence for
the associated volume forms. In an effort to make the concepts clear, the
formalism is developed in steps with the model example of matter coupled to
heat considered at each level. Thus we discuss a model for heat flow, derive
the relativistic Navier-Stokes equations and discuss why the individual
dissipative stress tensors need not be spacetime symmetric. We argue that the
new formalism, which notably does not involve an expansion away from an assumed
equilibrium state, provides a conceptual breakthrough in this area of research
and provide an ambitious list of directions in which one may want to extend it
in the future. This involves an exciting set of problems, relating to both
applications and foundational issues.
