  Quantum turbulence deals with the phenomenon of turbulence in quantum fluids,
such as superfluid helium and trapped Bose-Einstein condensates (BECs).
Although much progress has been made in understanding quantum turbulence,
several fundamental questions remain to be answered. In this work, we
investigated the entropy of a trapped BEC in several regimes, including
equilibrium, small excitations, the onset of turbulence, and a turbulent state.
We considered the time evolution when the system is perturbed and let to evolve
after the external excitation is turned off. We derived an expression for the
entropy consistent with the accessible experimental data, that is, using the
assumption that the momentum distribution is well-known. We related the
excitation amplitude to different stages of the perturbed system, and we found
distinct features of the entropy in each of them. In particular, we observed a
sudden increase in the entropy following the establishment of a particle
cascade. We argue that entropy and related quantities can be used to
investigate and characterize quantum turbulence.
