We read this to mean that adding an amount of heat (ΔQ: negative if removing heat) will result in a concomitant increase in entropy (decrease if negative) with the bath temperature as the proportionality constant. Looking at this equation, the units of J/K for entropy (S) should make more sense.
Wait a minute! Did I just allow for the condition that entropy could decrease? Isn’t one of the fundamental rules of thermodynamics that entropy can never go down?
Almost right. The entropy of a closed system cannot decrease. But it can easily decrease locally at the expense of an increase elsewhere. You can re-stack books on the shelves after an earthquake, restoring order. But via exertion, you transfer heat to the ambient air in the process—increasing its entropy.