Main sequence , solar-like stars ( M \lesssim 1.5 M _ { \odot } ) have outer convective envelopes that are sufficiently thick to affect significantly their overall structure .
The radii of these stars , in particular , are sensitive to the details of inefficient , super-adiabatic convection occurring in their outermost layers .
The standard treatment of convection in stellar evolution models , based on the Mixing-Length Theory ( MLT ) , provides only a very approximate description of convection in the super-adiabatic regime .
Moreover , it contains a free parameter , \alpha _ { MLT } , whose standard calibration is based on the Sun , and is routinely applied to other stars ignoring the differences in their global parameters ( e.g. , effective temperature , gravity , chemical composition ) and previous evolutionary history .

In this paper , we present a calibration of \alpha _ { MLT } based on three-dimensional radiation-hydrodynamics ( 3D RHD ) simulations of convection .
The value of \alpha _ { MLT } is adjusted to match the specific entropy in the deep , adiabatic layers of the convective envelope to the corresponding value obtained from the 3D RHD simulations , as a function of the position of the star in the ( \log g, \log T _ { eff } ) plane and its chemical composition .

We have constructed a model of the present-day Sun using such entropy-based calibration .
We find that its past luminosity evolution is not affected by the entropy calibration .
The predicted solar radius , however , exceeds that of the standard model during the past several billion years , resulting in a lower surface temperature .
This illustrative calculation also demonstrates the viability of the entropy approach for calibrating the radii of other late-type stars .