[ABRIDGED] The purpose of this work is to evaluate how several elements produced by different nucleosynthesis processes behave with stellar age and provide empirical relations to derive stellar ages from chemical abundances. We derive different sets of ages using Gaia parallaxes for a sample of more than 1000 FGK dwarf stars for which he have spectra from the HARPS-GTO program. We analyze the temporal evolution of different abundance ratios to find the best chemical clocks. We find that [$alpha$/Fe] ratio (average of Mg, Si and Ti), [O/Fe] and [Zn/Fe] are good age proxies with a lower dispersion than the age-metallicity dispersion. Several abundance ratios present a significant correlation with age for chemically separated thin disk stars (i.e. low-$alpha$) but in the case of the chemically defined thick disk stars (i.e. high-$alpha$) only the elements Mg, Si, Ca and TiII show a clear correlation with age. We find that the thick disk stars are more enriched in light-s elements than thin disk stars of similar age. The maximum enrichment of s-process elements in the thin disk occurs in the youngest stars which in turn have solar metallicity. The slopes of the [X/Fe]-age relations are quite constant for O, Mg, Si, Ti, Zn, Sr and Eu regardless of the metallicity. However, this is not the case for Al, Ca, Cu and most of the s-process elements, which display very different trends depending on the metallicity. This demonstrates the limitations of using simple linear relations based on certain abundance ratios to obtain ages for stars of different metallicities. Finally, we show that by using 3D relations with a chemical clock and two stellar parameters (either Teff, [Fe/H] or stellar mass) we can explain up to 89% of age variance in a star. A similar result is obtained when using 2D relations with a chemical clock and one stellar parameter, being up to a 87% of the variance explained.
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