Tolkien's definiton of immortality differs slightly from yours Eol. Tolkien states that the Eldar are immortal, but Elvish immortality is not truly that because they are built of the same stuff as man and therefore must be able to die from wounds or apparently from great greif and weariness, i.e. Miriel. And also all elves would supposedly start to weary and wane in Middle Earth which was very apparent in Cirdan.
Arwen was not a man or an elf, but a half-elf if that is what you mean. She was given the life alloted to elves until her decision was made, but she was never truly immortal because she never made the choice to follow her father when he went into the West and only if she had would she have been.
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