Name of quantity that is not invariant, but only changes in one direction

Question

How do you call a quantity that is not an invariant, but only changes in one direction during the process?

Example: The degree of the polynomials go down when Euclidean division is applied, so the algorithm stops.

Another example would be entropy.

Answer 1

You could say monotonic, or if you want to be more precise, (strictly) decreasing or (strictly) increasing.

Answer 2

If your process is continuous, then monotonic increasing (decreasing) is the right word. For example the function graph of $f(x) = 2x + 1$ is monotonic increasing.

In your example with polynomial degrees it is a discrete process an so the word descending (or ascending) is more adequate in my opinion.

Answer 3

The term I know is "monovariant," but I mostly only seen this term used in the context of contest math. See, for example, these notes.