  The quantum Fisher information (QFI) associated with a particular process
applied to a many-body quantum system has been suggested as a diagnostic for
the nature of the system's quantum state, e.g., a thermal density matrix vs. a
pure state in a system that obeys the eigenstate thermalization hypothesis
(ETH). We compute the QFI for both an energy eigenstate and a thermal density
matrix for a variety of processes in a system obeying ETH, including a change
in the hamiltonian that is either sudden (a quench), slow (adiabatic), or
followed by contact with a heat bath. We compare our results with earlier
results for a local unitary transformation.
