Résumé
Context. Modeling the convection process is a long-standing problem in stellar physics. To date, all ad hoc models have relied on a free parameter, α , (among others) that has no real physical justification and is therefore poorly constrained. However, a link exists between this free parameter and the entropy of the stellar adiabat. There are existing prescriptions, derived from 3D stellar atmospheric models, that treat entropy as a function of stellar atmospheric parameters (effective temperature, surface gravity, and chemical composition). This can offer sufficient constraints on α through the development of entropy-calibrated models. However, several questions have arisen as these models are increasingly used with respect to which prescription should be used and whether it ought to be used in its original form, along with the impacts of uncertainties on entropy-calibrated models. Aims. We aim to study the three existing prescriptions in detail and determine which of them demonstrate the most optimal performance and how it should be applied. Methods. We implemented the entropy-calibration method into the stellar evolution code (Cesam2k20) and performed comparisons with the Sun and the α Cen system. In addition, we used data from the CIFIST grid of 3D atmosphere models to evaluate the accuracy of the prescriptions. Results. Of the three entropy prescriptions currently available, we determined the one that has the best functional form for reproducing the entropies of the 3D models. However, the coefficients involved in this formulation must not be taken from the original paper because they were calibrated against a flawed set of entropies. We also demonstrate that the entropy obtained from this prescription should be corrected for the evolving chemical composition and for an entropy offset different between various EoS tables. This must be done following a precise procedure to ensure that the classical parameters obtained from the models are not strongly biased. Finally, we provide a data table with entropy of the adiabat of the CIFIST grid, along with the fits for these entropies. Conclusions. Thanks to a precise examination of entropy-calibrated modeling, we are able to offer our recommendations with respect to which adiabatic entropy prescription to use, how to correct it, and how to implement the method into a stellar evolution code.