Non-equilibrium Approach To Thermodynamics Using Jarzynski Equality and Diagonal Entropy

We combine the formalisms of diagonal entropy and Jarzynski Equality to explore thermalization effects. Applying this approach to a quantum harmonic oscillator, the diagonal entropy suggests 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 how to estimate temperature, entropy and measure work distribution functions. This technique offers a path to study the non-equilibrium quantum dynamics by means of performing work in a series of quenches.