  In this work, we study the applications of entropy bounds in two toy
cosmological models with particle production (annihilation), i.e., a
radiation-dominated universe and a dust-dominated universe. We consider the
co-moving volume and the volume covered by the particle horizon of a given
observer as the thermodynamic systems satisfying entropy bounds. For the
Bekenstein bound and the spherical entropy bound, it is found that the
cosmological singularity can be avoided and cosmological particle production
needs to be truncated in some special cases. Our study can be extended to other
cosmological models with particle production.
