  We address the statistical orthogonality catastrophe induced by a local
quench in the Aubry-Andr\'e model from the perspective of nonequilibrium
thermodynamics. We study the average work and the irreversible work production
when quenching the impurity potential in proximity of an orthogonality event.
We show how this description is able to capture the level crossings generating
the orthogonality and the avoided crossings which causes the plateau-like
structures, signature of the Aubry-Andr\'e spectrum, when considering the full
statistics of orthogonality events.
