An increase of entropy is less at higher temperatures. Is the inverse true for a decrease of entropy?

Question

So I have seen previous posts about how a change in entropy is relative to the temperature, and that an increase of entropy is less at a higher temperature, as explained by:

$$\Delta S_{\text{surrounding}} = -\frac{\Delta H_{\text{system}}}{T}$$

However, would it be appropriate to claim the opposite, that a decrease in entropy (where $\Delta H$ is positive) is less at lower temperatures than at higher temperatures? Would it still be relative, such as in the case of an increase of entropy? I am asking this from a chemistry perspective from a chem course.

My reasoning is that a decrease in entropy should be larger at higher temperature. For instance, a riot becoming peaceful is a much larger decrease in 'entropy' versus a peaceful meeting leaving the room. But the math points the other way.

Answer 1

The formula given makes no assumptions about the sign of $\Delta H$. For a fixed amount of heat, the change in entropy is smaller at larger temperatures, be it an increase or a decrease. Comparing entropy to disorder is just an analogue and should not be taken too literally