Often in movies, it is shown that a human body can possess an incredible amount of energy by bio-experiments. However, is there a proved maximum energy limit an average human can possess without any experiments, but just naturally by eating and working out?
While there is not a hard, specific number for the maximum "energy" a human can exert, there are limitations due to the basic physics laws of the universe. Yes, over time, humans have pushed performance limits, but not to the levels portrayed by superheroes in fiction. As the body consists of organic components, each of those components has strength limits, as well as energy expenditure limits based on the conversion of nutrition into energy used to perform work.
How is this maximum energy measured? Just take a look at sports metrics; the fastest mile, the longest jump, weightlifting records... Until a new record is set, the current recorded maximum energy is that specific record in that activity.
Through science and evolution over the long term, humans will be able to perform at higher and higher levels.
If you're referring to energy produced in an environment, like when they did lab experiments having different rankings of cyclists pedal to see how much power they have over an hour, then no, there is no way to test this as a better cyclist may be born every year. Most people have a maximum genetic potential. Whether or not you're an athlete you are limited by what your body can do. This is why we all can't look like professional bodybuilders. In the lab experiment most elite cyclists had about 25 watts per kg while amateurs had about 5-6 watts per kg. These cyclists also don't account for other forms of producing power that don't involve pedaling, etc. I think we are also limited by our anatomy and how quick our body moves, etc., but I assume since the best of the best cyclists all managed to get roughly 25 watts per kg, then this is probably close to what a human cyclist could do at their maximum. Then again, 30 years from now there may be a cyclist that beats this.