The travel demands caught Mrs. Clinton by surprise, especially in an era in which American officials can communicate via videoconference calls. But the technology, she has said, paradoxically puts a bigger premium on actually showing up. And Mr. Obama has traveled abroad sparingly, raising the pressure on her to do more.

On many trips, Mrs. Clinton flew overnight and, after landing, went straight into a 12- or 16-hour day, sometimes getting a quick shower at the American ambassador’s residence. On a visit to South Asia in 2009, she spent three consecutive nights on her plane, an Air Force Boeing 757, which is equipped with a small cabin and a bed.

Unlike Ms. Rice, who is seven years her junior, Mrs. Clinton is not an exercise enthusiast. And her diet over the past four years has been a mix of exotic fare in distant capitals and airplane food. While the military stewards often prepared a bowl of cereal and berries, Mrs. Clinton faced her share of breakfast burritos.

“On these trips, you’re in all these different time zones, your body clock is way off schedule, you’re not routinely getting exercise, and you’re not eating healthy food,” said Lissa Muscatine, a former speechwriter who traveled with Mrs. Clinton. “On top of that, she has to be operating at the height of mental acuity at all times.”