I recently studied duality in optimization where a primal optimization problem can be casted as a dual problem which provides meaningful lower bounds on the primal. There is also a notion of conjugate variables in mechanics (velocity/momentum) and thermodynamics (energy/temperature or pressure/volume for example) via the Legendre transform. Are these two related, if so how?
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1Related: https://physics.stackexchange.com/q/103997/2451 – Qmechanic Mar 15 '22 at 09:19