About the physics of transmutation in FMA:B Anyone who has watched even an episode of FMA or FMA:B knows how transmutations work. They are the staple of alchemy, and are very important to the show. The only rule with transmutations is the Law of Equivalent Exchange. This all seems fine and dandy when it is first explained to you; you must put in what you want to get out.

However, I soon started to considering the ramifications of this theory. Yes, it agrees with the Conservation of Mass, which states that matter cannot be created nor destroyed in a reaction. Sticking with chemistry and physics, it is also well-known that energy is required to make and break chemical bonds. While Edward provides ample matter for his transmutations (which are essentially 'reactions' in the parallel universe of FMA/FMA:B), where does he get the energy? If the Law of Equivalent Exchange was truly correct, wouldn't Ed and Al have to provide the equivalent amount of energy to bond all of the required substances together? Is this 'shortcoming' ever discussed in either series (2003 or 2009), or in the manga?
You can find a lot of explanations about the energy in Fma wikia.


  In the 2003 anime, though it is never outright explained from where
  the energy in transmutation comes, alchemists who attempt to create
  objects outside their range of skill are left exhausted, suggesting
  that at least some of the energy comes directly from their bodies. At
  the end of the anime series, it is explained that the energy powering
  transmutation is actually the energy of departed human souls passing
  through The Gate to the alchemical world from our world, negating the
  concept of Equivalent Exchange altogether.


That's one of the reasons some alchemists want the philosopher's stone, since it contains a lot of human souls, it can generate a lot of energy that one alchemist can't generate on his own.