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Combining the second-order entropy flow vector of the causal Israel-Stewarttheory 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, weinvestigate generalized equilibrium states for cosmological fluids withnonconserved particle number. We calculate the corresponding equilibriumparticle production rate and show that this quantity is reduced compared withthe results of the previously studied first-order theory. Generalizedequilibrium 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 aof the Robertson-Walker metric and may be regarded as a realization ofso-called K-matter.Comment: 17 pages, iopfts.tex file, submitted to Class. Quantum Gra

Generalized equilibrium of cosmological fluids in second-order thermodynamics