A creature on my world can draw in energy from the sun and convert it into chemical energy with 100% efficiency. For the purposes of this question assume the animal has similar structure to a (photosynthesising) lynx. If we assume it has practically infinite energy can anybody give me some information on how much stronger, faster and so on the creature would be. I assume it would still have limits otherwise there would be some form of muscle damage or would that be wrong?
Why isn't a (real) lynx as fast as a cheetah or as strong as a tiger?
The reason is the ecological niche that it occupies. The limits on lynx's speed and strength are a matter of evolutionary optimisation to a particular habitat. The big game hunting niche was occupied by saber toothed cats (etc) and the lynx evolved to hunt middle sized prey. Bigger and stronger lynx were less adapted to the environment.
Now if it can photosynthesize, it has an alternative energy source. This doesn't provide it with enough energy to survive. An active animal needs more energy than the sun provides, even at 100% efficiency. It could maintain its hunting rate, and use the additional energy to build bigger muscles. Alternatively, it could just hunt less, and spend the gain time looking for mates.
A 20kg Eurasian lynx probably needs about 5000 kJ per day (using a domestic cat as a model). Sunlight could probably provide about 1000kJ (using an optimistic estimate of the amount of sun the animal can be exposed to). Using photosynthesis would help the animal, but it wouldn't create a super-beast, and it might not make any difference unless there was an evolutionary niche available.
(maths: a cat needs about 30kcal per pound. A 20kg lynx is about 40lb so would need about 1200 kcal = about 5000kJ. Direct sunlight is about 1kW per m2, but at the latitude that lynx live, only about 50 $W/m^2$ actually reach the ground, and lynx like to live in forests so reduces a little. The area of a lynx (modelled as a 100cm x 30cm rectangle) is 0.3$m^2$, so a lynx gets about 15 W = 15 Joules per second. Over a day (24 hours since the average insolation was calculated over a full day) that is 1300 kJ, reduce that a little since the lynx lives in partial shade, but be generous -> 1000kJ )
It may not have any extra strength (etc) at all, because the strength (or other abilities) are not directly or even necessarily related to the ability to metabolise energy or abundance of energy.
The main reason is that most limits are not energy related. If you had infinite energy on tap immediately, your muscles would not automatically be stronger muscles, have a higher breaking strain for muscle fibres, be more efficient at conveying that energy to the muscles or removing excess heat or waste products (lactic acid etc) from them. It wouldn't necessarily make you any more intelligent or more co-ordinated, so even if your body could move faster or better (how?) you might not have the enhanced body-eye coordination or reaction speed required to do wonders with it.
In effect the question can be paraphrased a bit like this - if you could direct any amount of glycogen/ATP/whatever around your body at will, would you expect this to make you a superhuman? Probably not. Energy sounds great but its not the major limiting factor to performance.
Well, it doesn't have infinite energy. It has some limit on the rate it can gather energy, due to its limited surface area, and on the amount it can store, because of its finite mass. It also has a limit on the rate it can use its stored energy, because it has to avoid overheating and cooking itself.
So I'd give it, say, 30-50% greater strength and speed, in short bursts, without needing to eat a lot more (and don't look at that too hard, because the energy density of sunlight is pretty low). That's probably about as good as it gets while you're being at all science-based.