  We combine the formalisms of diagonal entropy and Jarzynski Equality to study
the thermodynamic properties of closed quantum systems. Applying this approach
to a quantum harmonic oscillator, the diagonal entropy offers a notion of
temperature for closed systems away from equilibrium, and allows computing
free-energy profiles. We also apply this approach to a hard-core boson lattice
model, and discuss measures how to estimate temperature, entropy and measure
work distribution functions. This technique offers a path to investigate the
non-equilibrium quantum dynamics by means of performing work in a series of
quenches.
