Direct, address, devote, apply are comparable when used reflexively with the meaning to turn or bend one’s attention, energies, or abilities to something or when meaning to turn, bend, or point (as one’s attention, thoughts, or efforts) to a certain object or objective.
Between direct and address there is often no perceptible difference; thus, one directs or addresses oneself to a task, or to his work, or to the study of a problem; one directs or addresses one’s attention to a certain thing, his remarks to a given person, his book to a special type of reader; also, one directs or addresses a letter when he writes on the envelope the name of the recipient and the place of delivery.
There is, however, a tendency to prefer direct when an intent or aim is implied or indicated and address when an appeal to the mind or feelings is expressed or understood.
Devote often adds to direct and address the implication of persistence; thus, one devotes himself to a task, a work, or the study of a problem when he resolutely continues towards its completion; one directs his attention to a problem but devotes his energies to its solution.
Quite as often, and in distinction from the other words, devote implies dedication or setting apart for a certain end or use.
Apply distinctively suggests concentration. One applies himself to a task or to his work when he gives his entire attention to what he has directed or addressed himself. In idiomatic use apply oneself and apply one’s mind often equal “concentrate” or “give one’s entire attention”.