  In this article a correspondence has been established between the momentum
dependent relaxation time approximation (RTA) solution of relativistic
transport equation and the thermodynamic field redefinition recently proposed
by P. Kovtun for relativistic hydrodynamic theory. Here, it has been shown that
the out of equilibrium energy density and hydrodynamic velocity follow an
extended matching condition indicating the fact that for an out of equilibrium
system quantities such as local temperature and flow velocity are not uniquely
defined and are subjected to include dissipative effects from the medium. Each
such matching condition which relates to separate choice of hydrodynamic frames
has been shown to correspond to a particular momentum dependence of relaxation
time in the relativistic transport equation. The thermodynamic identities
incorporating such extended matching have been shown to conserve the
energy-momentum tensor perfectly up to second order of gradient expansion under
momentum dependent RTA.
