Nonlinear response of the irreversible work via generalized relaxation functions

The nonlinear response of the excess work, when made via series expansion in the parameter perturbation of the average thermodynamic work, requires adjustments to agree with the Second Law of Thermodynamics. In this work, I present a well-behaved nonlinear response of the irreversible work, based on its well-known cumulant series expansion. From the generalization of the fluctuation-dissipation relation derived from it, I define the terms of the series expansion in the parameter perturbation of the irreversible work by the terms of the cumulants. Since every cumulant depends on raw moments, I define from them the generalized relaxation functions, whose arbitrary constants were chosen guaranteeing the accomplishment of the Second Law of Thermodynamics. A procedure to calculate the nonlinear response of the irreversible work is then provided.