Whenever I read about entropy in the context of philosophy, I see examples such as "the smoke doesn't go back into the cigarette" and "the toothpaste doesn't go back into the tube." This makes me wonder: don't these examples ignore the fact that much more order was created to make the cigarette and toothpaste (gathering and putting together the disparate raw materials, creating and maintaining the required machinery, etc.) than is lost by smoking or squeezing out the toothpaste?
Consider these as closed systems, including the chemical energy involved in squeezing, the light radiated by smouldering. Could you get them back, from those outputs? The key is the whole system. Yes disorder was created to make the ordered cigarette or tube.
It's like the ordered bit is the cool part of the fridge - it can't cool the room as a whole, because the fins at the back are releasing a more than balancing amount of heat. We can move order and disorder around, but in total the disorder increases.
Another way to describe entropy is to say it's spreading out of energy, the most spread out usually being heat. In quantum terms, it is the movement from pure to mixed states, a highly correlated/concentrated state like, all the coins the same way up in a stack, to a mixed state, like each coin is randomly heads or tails spread over the floor. Once you go to systems with order 10^23 coins the predictions how it will evolve get very strong.
Have a look at Maxwell's Demon for one of the more slippery problems with entropy, which links it squarely to information.