  The calculation of observable averages in non-equilibrium regimes is one of
the most important problems in statistical physics. Using the Hamiltonian
approach of nonlinear response theory, we obtain a series expansion of the
average excess work and illustrate it with specific examples of thermally
isolated systems. We report the emergence of non-vanishing contributions for
large switching times when the system is subjected to strong driving. The
problem is solved by using an adapted multiple-scale method to suppress these
secular terms. Our paradigmatic examples show how the method is implemented
generating a truncated series that obeys the Second Law of Thermodynamics.
