# Can the increase of entropy be decreased?

I know in an isolated system entropy always tends to increase, but what about the speed of that increase (e.g. the acceleration of entropy-the derivative of its speed)? Is there any law or relation giving the rate of that increase? Can it be decreased? (I am not asking here about a way to decrease entropy itself but its rate of increase-is it always increasing, too, is it constant, or can it be decreased?) Also, is there any difference in the answer of the question if it is asked for isolated and for non-isolated (both closed and open) systems?

Can anybody show me any links to work done on the subject? Or if there isn't any such work explain me what are the reasons why nobody has tackled the issue up until now (e.g. impossibility of experimental verification, lack of theoretical framework to put the question in, difficulty to make a sound mathematical model and so on)?

• I believe your first statement should say "isolated system". A closed system can exchange heat with its surroundings, so it can be cooled and experience a decrease in entropy (although this might just be different definitions). – John Mar 3 '17 at 21:11
• In addition, the entropy will not increase indefinitely. It will reach a maximum eventually, so I guess a quick answer to your question is that yes, the rate of increase will eventually decrease to zero. – John Mar 3 '17 at 21:12
• Thank you for the remark, I will correct it in a minute. Just wait a little bit. The mistake is on my side. – Yordan Yordanov Mar 3 '17 at 21:15
• Is it better now? – Yordan Yordanov Mar 3 '17 at 21:20
• Entropy is only always increasing for isolated systems. There is no such restrictions on entropy if your system is either open or closed. Also, I have just said that the rate of increase will decrease to zero eventually. – John Mar 3 '17 at 21:26

However, I understand your question. Imagine a bottle with some gas trapped inside that you might prepare as an isolated system in equilibrium with an entropy $S_1$. Then, if the gas is released to let fill the entire room, after some time, it will reach again the equilibrium with an entropy $S_2>S_1$. As I said before, you can only have entropy at the initial and the final states, because there is no equilibrium intermediate state, therefore there's no rate of change in the entropy. In addition, that system had changed its entropy because it wasn't isolated, there had to be some external agent to open the bottle. Right?