Eventually refers to an unspecific time when something will be completed, and it usually suggests it won't be done soon.

Think of eventually being said with a big sigh, as though the speaker knows that it will take a long time before something will be finished. Still, it does allow for the hope that, although it might not be anytime soon, it will be done at last — a promise fulfilled. Not now, maybe, but eventually.

Definitions of eventually
  1. adverb
    after an unspecified period of time or an especially long delay
    synonyms: finally
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