Speed of Entropy change

Question

If time in systems moving with different speed goes differently, does speed of entropy change differ in these systems? (is "speed of entropy change" a valid term? can we compare them?)

Answer 1

Entropy is an invariant $S \rightarrow S' = S$, whereas time is not, in general. Therefore the rate of change of entropy (this is the correct term) is a frame dependant quantity.

$$\frac{\mathrm{d} S}{\mathrm{d} t} = \gamma \frac{\mathrm{d} S'}{\mathrm{d} t'} = \gamma \frac{\mathrm{d} S}{\mathrm{d} t'}$$

with $\gamma$ the time-dilation factor.

Answer 2

I'd like to add to juangra's answer an illustration I bet you are familiar with. Remember the twin paradox? One brother gets older while the other stays young. That's precisly means that one brother's entropy changed more then the others.