A little thermodynamics lesson, which everyone probably knows without even realizing it!: "Cold" is just atoms moving slower than "hot". Temperature is essentially just the rate of movement of the atoms making up whatever is hot or cold. This is why refrigeration works. It slows the rate of bacteria growth on your food. Similarly, locking your food in airtight containers keeps new airborne bacteria from affecting your scrumptious vegan stuffing.
So, how long will that stuffing and those awesome rye rolls be good for?
3-4 days seems to be the most agreed upon by sources such as How Stuff Works and the Mayo Clinic. The colder and more air restricted the food is the longer it can last. In the physics field of thermodynamics, the Third Law of Thermodynamics states that when the temperature of a body (system) is absolute zero (the coldest temperature ever possible) the entropy (disorder of the system) is, also, at zero. Essentially, the colder a body is the less it's atoms move around. The less movement means the longer it will stay preserved as a tasty treat.