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I want to make the animation of the displacement to collide with the cooking pot, I already set the two objects with rigid body physics but it just goes through
No, modifiers themselves cannot collide. You need to apply them first and then apply collision to the modified object.
See Vertex Groups. There are plenty of postings here at BSE to be searched.
By selecting the top of the delicious tuna fish casserole in Edit Mode and making it into a vertex group named say "TCTOP" you can displace only exactly the top of mesh.