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What is the formal definition of energy in physics?

My question is what is the definition of energy in physics in general ? Moreover is energy a naturally occurring quantity or is a term defined in theoretical physics, ( for example force is somewhat a naturally occurring and not a defined quantity, whereas work is defined term)?

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    $\begingroup$ @BijayanRay There is no formal definition of energy in the mathematical sense you're looking for. This is physics, not math. The Noether charge 'definition' ACuriousMind talked about above is as rigorous as you can get. $\endgroup$
    – Avantgarde
    Commented Mar 31, 2019 at 14:52
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    $\begingroup$ @BijayanRay Energy as the ability to do work is a poor man's definition. No one uses that definition beyond high school. $\endgroup$
    – Avantgarde
    Commented Mar 31, 2019 at 16:36
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    $\begingroup$ @BijayanRay What ACuriousMind wrote above. $\endgroup$
    – Avantgarde
    Commented Mar 31, 2019 at 17:12
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    $\begingroup$ "Energy as the ability to do work is a poor man's definition. No one uses that definition beyond high school." Nonsense. That was the underlying definition of energy for over 200 years. It wasn't until Emmy Noether that this definition was replaced by something actually better. $\endgroup$ Commented Mar 31, 2019 at 18:54
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    $\begingroup$ @dmckee That's what I meant. So how is that nonsense, exactly? I don't see anyone using that old 'definition' in a random arxiv paper today. $\endgroup$
    – Avantgarde
    Commented Mar 31, 2019 at 22:55

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