Actually Kubo established early on (I think it was in the flashback to Renji & Rukia's childhood) that needing to eat is the basic sign that a soul has the potential to become a Shinigami.
Shut up you're all trying to ask questions that need not be answered. Let's all be happy that Aizen is finally after two years going to die. and hopefully Yammy will go soon too.
Certain hollows can live off the reishi in the air alone. Other beings like shinigami can forcefully tear apart an object to fuel their own power. The final form of the quincy is even more efficient at this task.
It can be assumed that a being as powerful as Ichigo can subconsciously tear apart the fabric of nearby objects and break it down to base reishi to sustain himself during extended periods of time.
