# Abstract, generic derivations of energy

How generic can be derivation of energy?

In a system with gravity and masses – it is potential energy and kinetic energy.

What if a constraint would be specified that no mass and velocity should be allowed (or possible) to use? For example, suppose there is a system of massless particles. Is there a way to define and use energy in such system? If yes, then how?

In general, I am dealing with abstract systems, where no typical gravity and mass occur. So it is hard for me to use potential and kinetic energy. Yet, I think it is possible to define an energy in such system, a kind of intensity of a process. Is there such thing defined in physics? What are most abstract derivations of energy?

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You put the "Hamiltonian-mechanics" tag, so you know the answer. If your equations of motion are derived from an Hamiltonian, then the Hamiltonian can be considered as an "energy", –  yohBS Feb 10 '12 at 15:40
Suggestion to the question(v1): Replace the phrase derivation of energy with definition of energy. –  Qmechanic Mar 11 '12 at 17:58
Lagrange/Hamiltonian work well when there is motion and conversion between Kinetic and Potential energy. The question is nice (and I feel that something is missing in the canonical viewpoints). –  Helder Velez Mar 12 '12 at 0:30