In general references to objects can be compared with == or !=, that is they do or do not refer to the same thing. And that's all: there is no well defined concept of reference value ordering. (as there might be if references were pointers to memory locations as they are in some other languages.)
That's references, but what about the things they reference? These things (instances of String, Double, Point etc) have an equals() method that will test whether the things should be considered equal. And they sometimes
have a method that allows one thing to be compared to another. Classes that do have a method allowing their instances to be compared implement the Comparable
interface. Some classes (like String and Double) do implement Comparable, and some (like Point) do not.
It is also possible to write a class which implements the Comparator
interface. Basically such a class would implement a method like the one you describe. You would write such a method yourself: ie there is no built in support for such comparisons (for the reason mentioned). Writing classes with such a method (ie that implement comparator) is discussed in Oracle's Tutorial in the Object ordering
page of the Collections trail.