Conservation of energy

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The law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be conserved over time.^[1] In the case of a closed system the principle says that the total amount of energy within the system can only be changed through energy entering or leaving the system. Energy can neither be created nor destroyed; rather, it can only be transformed or transferred from one form to another. For instance, chemical energy is converted to kinetic energy when a stick of dynamite explodes. If one adds up all forms of energy that were released in the explosion, such as the kinetic energy and potential energy of the pieces, as well as heat and sound, one will get the exact decrease of chemical energy in the combustion of the dynamite.

Classically, conservation of energy was distinct from conservation of mass. However, special relativity shows that mass is related to energy and vice versa by ${\displaystyle E=mc^{2}}$, the equation representing mass–energy equivalence, and science now takes the view that mass-energy as a whole is conserved. Theoretically, this implies that mass can itself be converted to energy, and vice versa. However, this is believed to be possible only under the most extreme of physical conditions, such as likely existed in the universe very shortly after the Big Bang or when black holes emit Hawking radiation.

Given the stationary-action principle, conservation of energy can be rigorously proven by Noether's theorem as a consequence of continuous time translation symmetry; that is, from the fact that the laws of physics do not change over time.

A consequence of the law of conservation of energy is that a perpetual motion machine of the first kind cannot exist; that is to say, no system without an external energy supply can deliver an unlimited amount of energy to its surroundings.^[2] Depending on the definition of energy, conservation of energy can arguably be violated by general relativity on the cosmological scale.^[3]