New York has not had a case proceed to the arbitration stage since 2008, when it defeated Chien-Ming Wang.
Carpenter, 29, was acquired from the Braves in a New Year's Day trade and projects to handle the sixth or seventh innings. He was 6-4 with a 3.54 ERA in 65 appearances for Atlanta last year, owning a 3.62 career ERA in 188 games over four big league seasons.
Eovaldi, who turns 25 in February, came to the Yankees in a Dec. 19 trade with the Marlins and will slot at the back end of the rotation. He was 6-14 with a 4.37 ERA in 33 starts for Miami last year, logging 199 2/3 innings and permitting a National League-leading 233 hits. Eovaldi owns a 4.07 ERA in 83 career big league games (79 starts) dating back to 2011.
Pineda, who turns 26 on Sunday, made 13 starts in his first season of on-field duty with the Yankees, going 5-5 with a 1.89 ERA while missing more than three months with a right shoulder injury. In 76 1/3 innings, Pineda issued just seven walks and struck out 59 batters while holding opponents to a .200 average.
Bryan Hoch is a reporter for MLB.com. Follow him on Twitter @bryanhoch and read his MLBlog, Bombers Beat. This story was not subject to the approval of Major League Baseball or its clubs.