Is there a linear connection between muscle size and the power it can produce? If not, why? And what is the true correlation if any, can it be described with an appropriate function? What other factors modify it? (Red/white fiber for instance?)
The short answer to your question is that the work output from a muscle is a combination of physiological cross-sectional area, length, fiber type, and recruitment (how many motor units are activated).
Read on for more details.
Force output (tension) of a muscle is proportional to its physiological cross sectional area (Fundamental of Medical Physiology), and shortening is proportional to the length of the muscle. Work output (force X length) is a function of both. Power (work / time) involves both force, length change, and the shortening velocity. Shortening velocity is related to muscle fiber types.
There is a complex relationship between force output and length. In the graph below, the x-axis is relative length (1.0 being resting). When muscles operate outside a relatively narrow range (gray box), the cross-bridges are either too close together or too far apart to optimally generate force. When the muscle gets really stretched, force goes up, but only because passive tension (the intramuscular connective tissue is getting stretched) increases.
The force-velocity curve below relates relative force output to how fast the muscle is shortening (which can be negative; i.e., lengthening contraction). The green part of the curve is muscle shortening. As velocity approaches 0, the muscle produces maximal shortening force. When the muscle goes into the red part of the curve, force is even higher. In order for a muscle to shorten very quickly, it can't produce a lot of force (far right).
Muscle fiber type generally relates to both the force output of a muscle fiber and it's shortening velocity. There are different ways to classify muscle fibers (enzyme activity, myosin isoform, or the "classical" method):
SO ("slow oxidative"; the dark meat of a chicken) fibers contract slowly, produce lower force but are fuelled by oxidative reactions and thus have good endurance. At the other end of the spectrum, FG ("fast glycolytic"; the white meat of a chicken) fibers contract quickly with high force, but fatigue easily because they get energy from glucose, which is rapidly depleted. FOG fibers are intermediate between the two.
The muscular fiber cross section and length would be proportional to its strength, but there are also many different kinds of cellular types and structures which can result in muscles which are quicker or stronger, have better endurance etc.
This post from 2009 ago puts forward the hypothesis that chimpanzees, who weigh 70 to 130 lbs (32 to 60 kg) are typically capable of lifting 3-4 times more weight than a human being can. They also put forward that the coordination of the muscle with other muscle fibers makes up the gross difference in strength. Human beings have much better fine motor control for delicate operations than chimps, which might cause the muscles to be less in synch resulting in lower strength despite the fact that we have about the same amount (or less) of muscle tissues in say our arms or legs.