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The off-equilibrium response function $\chi (t,t_w)$ and autocorrelationfunction $C(t,t_w)$ of an Ising chain with spin-exchange dynamics are studiednumerically and compared with the same quantities in the case of spin-flipdynamics. It is found that, even though these quantities are separatelydifferent in the two cases, the parametric plot of $\chi (t,t_w)$ versus$C(t,t_w)$ is the same. While this result could be expected in higherdimensionality, where $\chi (C)$ is related to the equilibrium state, it is farfrom trivial in the one dimensional case where this relation does not hold. Theorigin of the universality of $\chi(C)$ is traced back to the optimization ofdomains position with respect to the perturbing external field. This mechanismis investigated resorting to models with a single domain moving in a randomenvironment.Comment: 24 pages, 7 figure

Universality of the off-equilibrium response function in the kinetic Ising chain