  We derive relativistic viscous hydrodynamic equations invoking the
generalized second law of thermodynamics for two different forms of the
non-equilibrium single-particle distribution function. We find that the
relaxation times in these two derivations are identical for shear viscosity but
different for bulk viscosity. These equations are used to study thermal
dilepton and hadron spectra within longitudinal scaling expansion of the matter
formed in relativistic heavy-ion collisions. For consistency, the same
non-equilibrium distribution function is used in the particle production
prescription as in the derivation of the viscous evolution equations.
Appreciable differences are found in the particle production rates
corresponding to the two non-equilibrium distribution functions. We emphasize
that an inconsistent treatment of the non-equilibrium effects influences the
particle production significantly, which may affect the extraction of transport
properties of quark-gluon plasma.
