  For systems performing a weakly isothermal process, the decorrelation time
dictates how fast the relaxation function decorrelates. However, like many
other thermally isolated systems, the transverse-field quantum Ising chain
presents an ill-defined decorrelation time. On the other hand, the Kibble-Zurek
mechanism uses a heuristic relaxation time to achieve its famous scaling. The
problem however of having a well-defined decorrelation time, derived from first
principles, agreeing with the Kibble-Zurek mechanism is still open. Such a
solution is proposed here by measuring the work using the time-averaged
relaxation function of the system, which offers a new and well-defined
decorrelation time for thermally isolated systems. I recover with this the
Kibble-Zurek mechanism in the finite-time and weak driving regime, and new
features in the slowly-varying one. The gain in control over the system in such
a distinction is desirable for potential applications.
