  Atomistic effective Hamiltonian simulations are used to investigate
electrocaloric (EC) effects in the lead-free Ba(Zr$_{0.5}$Ti$_{0.5}$)O$_{3}$
(BZT) relaxor ferroelectric. We find that the EC coefficient varies
non-monotonically with the field at any temperature, presenting a maximum that
can be traced back to the behavior of BZT's polar nanoregions. We also
introduce a simple Landau-based model that reproduces the EC behavior of BZT as
a function of field and temperature, and which is directly applicable to other
compounds. Finally, we confirm that, for low temperatures (i.e., in non-ergodic
conditions), the usual indirect approach to measure the EC response provides an
estimate that differs quantitatively from a direct evaluation of the
field-induced temperature change.
