  Combining the second-order entropy flow vector of the causal Israel-Stewart
theory with the conformal Killing-vector property of $u_{i}/T$, where $u_{i}$
is the four-velocity of the medium and T its equilibrium temperature, we
investigate generalized equilibrium states for cosmological fluids with
nonconserved particle number. We calculate the corresponding equilibrium
particle production rate and show that this quantity is reduced compared with
the results of the previously studied first-order theory. Generalized
equilibrium for massive particles turns out to be compatible with a dependence
$\rho \propto a ^{-2}$ of the fluid energy density $\rho$ on the scale factor a
of the Robertson-Walker metric and may be regarded as a realization of
so-called K-matter.
