For the small part of physics I know (Classical mechanics, Quantum mechanics, electrodynamics), everything can be derived from a variational principle. Variational principles are also well known for their practical applications, like in engineering calculations.
I would like to know if this is a deep fingerprint of physics or a general consequence from mathematics.
For example, it is clear why differential equations play a big role in physics, and it may well be that all differential equations can be derived from a variational principle. In this case, the role of variational principles would be a simple mathematical consequence.
On the contrary, if all differential equations cannot be derived from a variational principle, then the big role of the variational principles in physics would be a natural fact. Then its meaning would be worth to investigate.
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