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We aim to constrain the mixing processes in low-mass stars by investigatingthe behaviour of the Li surface abundance after the main sequence. We takeadvantage of the data from the sixth internal data release of Gaia-ESO, idr6,and from the Gaia Early Data Release 3, edr3. We select a sample of mainsequence, sub-giant, and giant stars in which Li abundance is measured by theGaia-ESO survey, belonging to 57 open clusters with ages from 120~Myr to about7 Gyr and to Milky Way fields, covering a range in [Fe/H] between -1.0 and+0.5dex. We study the behaviour of the Li abundances as a function of stellarparameters. We compare the observed Li behaviour in field giant stars and ingiant stars belonging to individual clusters with the predictions of a set ofclassical models and of models with mixing induced by rotation and thermohalineinstability. The comparison with stellar evolution models confirms thatclassical models cannot reproduce the lithium abundances observed in themetallicity and mass regimes covered by the data. The models that include theeffects of both rotation-induced mixing and thermohaline instability accountfor the Li abundance trends observed in our sample, in all metallicity and massranges. The differences between the results of the classical models and of therotation models largely differ (up to ~2 dex), making lithium the best elementto constrain stellar mixing processes in low-mass stars. For stars withwell-determined masses, we find a better agreement between observed surfaceabundances and models with rotation-induced and thermohaline mixings, theformer dominating during the main sequence and the first phases of thepost-main sequence evolution and the latter after the bump in the luminosityfunction.

The Gaia-ESO survey: Mixing processes in low-mass stars traced by lithium abundance in cluster and field stars