As far as our deep understanding of the universe is concerned, the greatest discovery in thermodynamics is the so-called ’second law’, which says that heat always flow from a hotter object to a cooler object when the two objects are placed in contact. It sounds blindingly obvious; yet this simple rule has been described as the supreme law of nature. Its tells us which way time flows, and that things wear out.
There are two classic examples which highlight the importance of this law. First, imagine a cup of coffee, into which you drop an ice cube. The ice cube melts, as heat flows from the hot coffee into the cold ice. You never, ever, see a cool cup of coffee start to get hotter, all by itself, while an ice cube grows in the middle of the cup. This is what we mean by saying that the second law defines the arrow of time. If you made a film of the melting ice cube, and ran it backwards through a projector, everyone who watched the film would know it was running backwards.
There is also an example of things wearing out. A cup of coffee with an ice cube in it has more structure than a cup of cold coffee, just as a house has more structure than a pile of bricks. Like the melting ice cube, if you leave a house unattended for long enough it will turn into a heap of bricks. But no matter how long you leave a heap of bricks unattended, it will never form itself into a house. This kind of structure possesses a quantity of information. The lost structure is like lost information, because the cold coffee has no ‘memory’ of the fact that some of the liquid used to be an ice cube, just an a brick has no ‘memory’ that it used to be part of a wall.
Being slightly perverse, physicists actually measure information in a negative sense, and give negative information the name ‘entropy’. The second law of thermodynamics can be expressed most succinctly as saying that entropy always increases- things wear out, ice cubes melt, houses fall down, people die.
But there is one strange feature of all this which we ought to mention. The second classic example of the second law at work is based on imagining a box of gas with a partition in the middle. One half of the box can be pumped out, so that it is empty, with no atoms in it. The other half is full of atoms, tiny little spheres moving rapidly and bouncing off one another in accordance with Newton’s laws of motion. If we pull the partition out of the way, the atoms will spread out to fill up the entire box, and the temperature of the gas will fall as they do so. But if you start with a box full of gas, you will never see all the atoms move together up into one end of the box, leaving a vacuum in the other half.
Or will you? Boltzmann calculated that if the atoms are moving about at random there is, in fact, a very tiny chance that all the atoms in the box will happen to move together in this way. The chance of this happening is so small that it would take billions upon billions of years for it to happen. And this gives us another perspective on the universe. Low entropy states are possible, but they are extremely unlikely.
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In one of those early paper, published in 1903, Einstein thought that he has found a proof that the second law of thermodynamics must always hold. The second law, remember is the one that says things wear out. In modern language, Einstein thought that he had proved that the arrow of time is built into the laws of physics, although he never used that expression himself. But he had failed to appreciate one of the key points in Boltzmann’s argument, which jumped off from a comment made by Johann Loschmidt, and was published in 1877, in a paper Einstein cannot have read in 1903. This made it clear that the second law is not an absolute law of nature, but only has a statistical validity.
Remember the box of gas, one half full, the other empty, with a partition in the middle? We talked of pulling the partition out and letting the gas fill the box, then waiting for a very long time to see if the molecules of the gas might ever move together into one end of the box again. We said that, according to Boltzmann, this might happen, after a very, very long time. It would be as if we watched a pile of bricks, for a time much longer than the age of the universe, and suddenly it did assemble itself into a house. During such processes, the flow of entropy is reversed and the second law is violated- in the case of the gas in the box, the gas would get hotter as it squeezed itself into one end of the box. Time, by our everyday standards, would be running backwards.
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