# Is the conservation of energy a statistical phenomena?

mrspeedybob
Suppose you build a heat engine. On one side you have a hot body, on the other side you have a cold body. Between the 2 you have the heat engine but on a parallel path you have a simple heat conductor.

What will happen is that some of the heat will travel through and power the heat engine and some will travel through the heat conductor and do nothing until the 2 bodies are at the same temperature, but heat is just the magnitude of the random motions of atoms/molecules. It seems like it would be possible for random motions to result in heat transfer through the conductor until the hot body is hot again and the cold body is cold again, by pure chance. This would be so improbable that it would likely never be observed happening but I can't see a reason that it should be impossible.

Another scenario where extremely unlikely events could result in a violation of conservation of energy would be on the quantum level. It is my understanding that any given particle has a certain amount of inherent uncertainty in its position and momentum. If a significant percentage of an objects particles spontaneously and simultaneously decided they were going to exist a meter further up the gravity well from their current position that would be observed as a violation of the law of conservation of energy. Again, such an event would be so improbable that it would likely never be observed but improbable does not equal impossible.

So, as the title states, is the law of conservation of energy a fundamental law or the result of statistical probability?