A force is conservative when its work depends only on the endpoints. On a simply connected domain this is equivalent to for a potential energy .
A nonconservative force has path-dependent work. On a simply connected domain, a continuously differentiable force is nonconservative exactly when its curl does not vanish identically.

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Conservative force by Wikipedia Bot 1
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A conservative force is a type of force in physics that has the property that the work done by the force on an object moving from one point to another is independent of the path taken between the points. Instead, the work done depends only on the initial and final positions of the object. This means that if the object returns to its original position, the total work done by a conservative force over that closed path is zero.
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