The best example is a hot cup of
coffee. You walk into a coffee shop and check your pockets that yes, you do indeed have some coin of the realm that you spent time and energy to acquire somewhere else. This coin is therefore concentrated time and energy or effort. You then walk up to the counter and order (key word here) a hot cup of
coffee. The Barrista, who has an understanding of what you want, then reaches for a cup that someone spent time and effort making, and someone made an effort to
clean. He then pours in this fluid that contains pure (hopefully)
water that has been heated (we pay the power company for the
heat) and poured over these magic beans that came from far away, with many people involved with ships and trucks burning fuel so that these beans could arrive here. This cup of
coffee is indeed a highly ordered structure in the Universe. But today, instead of drinking it, we are going to perform an experiment. If we let the cup of
coffee sit on the table long enough, say 30 minutes, what happens? It gets
cold. The heat energy that we paid for is no longer concentrated in the cup. It still exists, but in the room not in the cup. This is a gain in entropy. If we let the cup of
coffee sit there long enough, say 4 days, we notice that some of the
water that we paid for has evaporated. It still exists as
water vapor in the room (probably attacking the wallpaper) but not in the cup. This too, is a gain in entropy. By this time the Barrista will probably come along to kick us out, after all we've been here 4 days and
haven't actually drank any
coffee. If he does kick us out then he will have to
clean the cup, spending time and energy and hot
water, to bring the cup back up to a useful higher energy state, ready for the next customer. This would be an example of negative entropy. But he had to spend more energy elsewhere to accomplish this.
But let's say he doesn't kick us out. If we are still sitting here watching the cup in about 30 years when the building falls over, breaking the cup, then this too is a gain in entropy.
I am one of the few people on the planet to tell you that negative entropy = life (localized), in thermodynamics this would appear in an equation as -Δs (pronounced minus delta s).
