In the era of large spectroscopic surveys, massive databases of high-quality spectra provide tools to outline a new picture of our Galaxy. In this framework, an important piece of information is provided by our ability to infer stellar ages. We aim to provide empirical relations between stellar ages and abundance ratios for a sample of solar-like stars. We investigate the dependence on metallicity, and we apply our relations to Gaia-ESO samples of open clusters and field stars. We analyse high-resolution and high-S/N HARPS spectra of a sample of solar-like stars to obtain precise determinations of their atmospheric parameters and abundances through differential spectral analysis and age through isochrone fitting. We investigate the relations between ages and abundance ratios. For the abundance ratios with a steeper dependence on age, we perform multivariate linear regressions, including the dependence on metallicity. We apply our relations to a sample of open clusters located in 4<R$_{GC}$<16 kpc. Using them, we are able to recover the literature ages only for clusters located at R$_{GC}$>7 kpc. In these clusters, the content of s-elements is lower than expected from chemical evolution models, and consequently the [s/$alpha$] are lower than in clusters of the same age located in the solar neighbourhood. With our chemical evolution model and a set of empirical yields, we suggest that a strong dependence on the star formation history and metallicity-dependent yields of s-elements can substantially modify the slope of the [s/$alpha$]-[Fe/H]-age relation in different regions of the Galaxy. Our results point towards a non-universal relation [s/$alpha$]-[Fe/H]-age, indicating the existence of relations at different R$_{GC}$ or for different star formation history. A better understanding of the s-process at high metallicity is necessary to fully understand the origin of these variations.
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