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Electrocaloric cooling, with the advantages of zero global warming potential, high efficiency, smart size, etc., is regarded as a promising next-generation technology for green refrigeration. The exotic negative electrocaloric effect (ECE) in antiferroelectric materials forms the basis to improve the caloric cooling power density, but the underlying mechanism remains elusive. By using a fully first-principles method, we successfully simulate the electric field-triggered structural phase transition from antiferroelectric to ferroelectric in a prototypical antiferroelectric material PbZrO3 (PZO). Through tracking the phonon entropy evolution and measuring the temperature-dependent polarization along the transition path, we disclose that the negative ECE in PZO originates from the latent heat associated with phonon entropy rather than the previously recognized dipolar entropy. Accordingly, a new concept of phonon entropy engineering is proposed that engineering the density of states especially for low-frequency phonons can modulate the phonon entropy, which provides an effective route to enhance the cooling power density. [ABSTRACT FROM AUTHOR]