  A relativistic kinetic description for the irreversible thermodynamic process
of gravitationally induced particle production is proposed in the context of an
expanding Friedmann-Robertson-Walker (FRW) geometry. We show that the covariant
thermodynamic treatment referred to as "adiabatic" particle production provoked
by the cosmic time-varying gravitational field has a consistent kinetic
counterpart. The variation of the distribution function is associated to a
non-collisional kinetic term of quantum-gravitational origin which is
proportional to the ratio $\Gamma/H$, where $\Gamma$ is the gravitational
particle production rate and H is the Hubble parameter. For $\Gamma << H$ the
process is negligible and as should be expected it also vanishes (regardless of
the value of $\Gamma$) in the absence of gravitation. The resulting
non-equilibrium distribution function has the same functional form of
equilibrium with the evolution laws corrected by the particle production
process. The macroscopic temperature evolution law is also kinetically derived
for massive and massless particles. The present approach points to the
possibility of an exact (semi-classical) quantum-gravitational kinetic
treatment by incorporating back-reaction effects in the cosmic background.
