Seonglae ChoFirst Law of Thermodynamics
Symmetry of physical laws under variation of the path in time
Principle of stationary action → Euler–Lagrange equation
Conservation of Energy
For a static empty universe
However, our universe is not globally symmetric with respect to time since spacetime itself evolves. Global energy conservation does not hold, even though local conservation () still applies.
Contracted Bianchi identities
Conservation of energy
In physics and chemistry, 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] 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.
https://en.wikipedia.org/wiki/Conservation_of_energy