When discussing this, rather than equating plants with humans and using terms like sleep and rest I think a better analogy would be cooking.
Yes, cooking. The chemical processes that takes place in say, cooking a Vegetable soup. For the Soup to cook infrared radiation is absorbed by the cells within the veg pot. A sort of metabolic process takes place with the exchange of sugars and in a given time the soup is done. You turn the stove off, the chemical process continues at least until the soup goes cold.
Now with a living plant it gets IR from our HID lighting. We turn them off,the metabolic process continues because it has plenty of sugars still stored with its cells.