We evaluate the gravity-induced negativity volume of the generalized Wigner
function in a hybrid system consisting of a particle in a two-localized
superposition state and an oscillator. The generalized Wigner function can
capture the nonclassicality of the system. The increase in the negativity
volume of the generalized Wigner function can be an indicator of the
entanglement generation, which is demonstrated in the hybrid system generating
the gravity-induced entanglement in various initial states. Moreover, by
comparing the behaviors of the negativity volume with the entanglement
fidelity, we show that the nonclassical feature of entanglement is properly
identified by the criterion based on the negativity volume of the generalized
Wigner function when the oscillator is initially in a thermal state.Comment: 12 pages, 5 figure