Is there a physics mechanism to explain how sunflowers rotate to always face the sun? I tried to find more information or references using google search, but no luck.
The physics is being explored in the rapidly growing field of biophysics. The short answer is that plants are able to move, in general, via hydraulic or osmotic processes.
Osmotic process describe the tendency of water to move into a solution via osmosis, where osmosis is "the movement of solvent molecules through a selectively permeable membrane into a region of higher solute concentration, aiming to equalize the solute concentrations on the two side." Hydraulic processes reflect the tendency of water to stay put and not move out of a solution. See here.
For instance, plants can better grow through hydraulic pressure, but respond rapidly to environmental changes (cf sunflowers), or food (cf venus fly trap) via osmotic mechanisms such as pumping across cell membranes (discussed in a recent article on the venus fly trap in Nature). In either case, the exact mechanics are still poorly understood and the subject of a lot of research. Plants that could move or adapt to environmental changes have obvious economic benefit.