In this answer to the question "why does the moon have the same rotation and revolution periods?", we read:
The mass and speed of rotation of the Earth influence the moon in that some of its rotational energy is actually transferred to the moon. (...) Many of the moons in the solar system have also reached this point of equilibrium. In Jupiter, the moons Amalthea, Thebe, Io, Ganymede, Callista, and Europa, all have identical rotational and revolutionary periods.
My two questions are:
Can we show the mechanics of this quantitatively?
Does the system Earth-Sun experience the same phenomenon, in some measure? Will then the earth slow down its rotation speed until it will show always the same face to the sunlight? In this last case, on which timescale?