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We study the impact of thermal hysteresis at the first-order structural/ferroelectric phase transitions on the electrocaloric response in bulk BaTiO₃ by performing molecular dynamics simulations for a first-principles-based effective Hamiltonian. We demonstrate that the electrocaloric response can conceptually be separated in two contributions: a discontinuous transitional part, stemming from the jump in entropy at the first order phase transition, and a continuous part, due to the change of polarization and entropy within each phase. This latter part increases with the strength of the applied field, but for small fields it is very small. In contrast, we find a large temperature change of ≈1 K resulting from the transition entropy, which is essentially independent of the field strength. However, due to the coexistence region close to the first order phase transition, this large electrocaloric response depends on the thermal history of the sample and is generally not reversible. We show that this irreversibility can be overcome by using larger fields.