The 133 Major League players who filed and their respective clubs will officially exchange salary figures by Friday.
Arbitration hearings will be scheduled to take place between Feb. 4 and Feb. 20, but players and clubs can also reach agreements on new contracts before then.
Hughes, who is in his third and final year of arbitration eligibility, could project to receive one of the largest salary increases of the group. The right-hander earned $3.2 million from the Yanks in 2012, going 16-13 with a 4.23 ERA in 32 starts.
Logan and Robertson both served important roles in the club's 2012 bullpen. Logan is in his fourth year of arbitration eligibility and earned $1.875 million last season, when he was 7-2 with a 3.74 ERA in a league-leading 80 appearances.
Robertson is arbitration-eligible for the second time and earned $1.6 million last season, going 2-7 with a 2.67 ERA in 65 appearances.
Chamberlain, who earned $1.675 million last season, missed much of the year to injury and thus will likely receive only a small increase. He was 1-0 with a 4.35 ERA in 22 appearances and is arbitration-eligible for the third time.
The Yankees have not been to a hearing since 2008, when they defeated pitcher Chien-Ming Wang with a $4 million offer. Wang had requested $4.6 million.