I think you're confusing multiple different concepts here. I'll let someone more versed in information theory weigh in on the black hole discussion, but ashes themselves are just the non-burnable parts of whatever you set on fire.

In a log, for example, the vast majority of the mass is water (which can evaporate into the air) and organic compounds that will be turned into carbon dioxide and carbon monoxide (this is the chemical reaction you are doing when you see fire). After you completely, 100% turn the organic compounds into gasses, you are left with ashes, which are largely the micronutrients that were stored in the plant and used to keep it healthy. Calcium, potassium, magnesium, iron.