This is not time symmetric, meaning that this law of entropy is not the same if you were to go backward in time and so it would be impossible within this law. If you add milk to coffee you will see it spread out across the coffee; this process will end with an increase in entropy. The reverse of this process would be the milk un-spreading and therefore the entropy decreasing, which violates the second law of thermodynamics. So the inverse of processes that occur in life and that are described above are not allowed, as they would cause a decrease in entropy, so this shows a distinct arrow of time for this system, as time is shown to be asymmetric.
Micro systems like chemical events are not defined by time in the same way as the macro systems; reversible reactions can run backward and forwards and can return to their original state.
Boltzmann said that entropy was just probability and was able to show that macroscopic distribution of high order and of low entropy could be made up of relatively little microscopic arrangement of molecules, so the likelyhood of these arrangements occurring randomly are relatively improbable. Systems do not tend to go into states that are less probable than the states they are already in, therefore order tends to go to disorder. There’s only a few ways to have a clean and ordered room and several ways to have a messy and disordered room, so a disordered room is more probable. For example if you had two boxes (X and Y) connected by a corridor and you fill room X with a gas, the gas will spread into box Y. The gas spreading in to box Y is a more probable state than the original state, as it is highly probable for the gas to spread. Although it is not impossible for the gas to return to the original state in the X Box, it is highly improbable.
So how does this relate to the arrow of time? The universe tends to disorder over time as it is more probable that it will disorder rather than order. Every process, system or event tends to either stay the same or increase in entropy and never decrease, so time must have a direction according to the second law of thermodynamic and its direction should run along side the increase in entropy. We know now that entropy can never decrease so in the future the entropy can not be less than what is it now, and today the entropy is more then yesterday. So if we were to stand on a time line and look back in to the past, we would be able to see that in the past the entropy is lower the it is today, we remember that is lower than today. If the second law were to apply to the past, then we would see an increase in entropy as we look back. This is contradicted by our experience and memories.
Whatever we do in our lives contributes to an increase in entropy. Even if I was to tidy up my room for once and restore its order, there still would not be a decrease in entropy. I would have used up energy to tidy that room, single-handedly increasing the temperature of the whole universe by doing so.
Some say that the past does not exist and therefore no laws can be applied to it. We have photos of events that occurred in the past but these photos are here with us and they are just documents in the present. If the past does not exist than an arrow in the direction of the past can not exist.
I guess if you were to step into a time machine and go to the past, you would experience a decrease in entropy with an increase in time (as perceived by you), which violates the second law. This would rule out any time travelling to the past, but travelling to the distant future would be acceptable as we travel to the future constantly anyway. Just do not expect there to be a return flight.
References:
Thermal Physics, Second Edition, C.B.P.Finn.
How To Build A Time Machine, Paul Davies
The Physical Basis Of The Direction Of Time, Fourth Edition, H.D.Zeh
The Character Of Physical Law Richard Feynman
Asymmetries Of Time Paul Horwich
Website References:
http://www.tardyon.de/7ursache.htm
