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The calculation of observable averages in non-equilibrium regimes is one ofthe most important problems in statistical physics. Using the Hamiltonianapproach of nonlinear response theory, we obtain a series expansion of theaverage excess work and illustrate it with specific examples of thermallyisolated systems. We report the emergence of non-vanishing contributions forlarge switching times when the system is subjected to strong driving. Theproblem is solved by using an adapted multiple-scale method to suppress thesesecular terms. Our paradigmatic examples show how the method is implementedgenerating a truncated series that obeys the Second Law of Thermodynamics.

Series expansion of the excess work using nonlinear response theory