  The Jarzynski equality (JE) is analyzed in regard to its validity for both
quasi-static transformations in the thermodynamic limit and Hamiltonian
evolutions of the work protocol. In the first case, we show that the JE holds
for isothermal transformations only; in the second case, we show that the work
done (linked to the final state Hamiltonian) depends on the temporal dynamics
of the work protocol (including its speed), thus precluding the possibility of
identifying it with the free energy or any other thermodynamic state function.
Even in the case of thermodynamic limit and infinitesimally slow
transformations of the Hamiltonian (adiabatic invariance) following states of
thermodynamic equilibrium, the resulting work expression does not default to
the JE, but to the work relation for adiabatic thermodynamic transformations,
W=Delta U, where W is work and U is internal energy.
