The properties of linear entropies for atom-field coupling system for atom and for field in the system are investigated via degenerate Raman two-photon coupling processes in a phase-damping cavity. The influences of atomic coherence and mean photon number on all the linear entropies are discussed. The results show the the existence of cavity phase damping leads to the phenomenon that the linear entropy of the system is larger than zero except the initial time and independent of the atomic initail preparation. When the atom is initially in its excited state or ground state, the linear entropy o...