Statistical Mechanics/The Foundations
This page may need to be [edit] Introduction
The goal of statistical mechanics is to bridge a gap that exists between the microscopic world and the macroscopic. A quantum physicist will tell you everything you want to know about a particle by itself. If you ask, he will even be able to give you the exact equations of motion for a system of two particles. However, once you add a third or more, things start to get a little bit hairy. There is no longer an analytic solution, and one must turn to computers to solve the problem numerically - and the results the computer will spit out are quite accurate for systems of 3, 4 or more particles. But what happens when the number of particles you have is much larger - not just ten or twenty, or even a thousand - what happens when you have a cup of water for example, with ~1025 particles? For each one of the 1025 particles, the computer would have to consider the 1025 interactions with every other particle - that's a total of 1050 interactions that would have to be computed at every instant! Even a computer that could perform a trillion calculations per second would take 1020 times longer than the age of the universe to compute the exact state of your cup of water for a single instant in time. Clearly such a computation is not possible. Quantum mechanics alone is not capable, in practice, of solving macroscopic systems.
Statistical mechanics provides the tools required to take the information given by quantum physics and use it to describe macroscopic systems and predict how they will evolve in time. By far the most important of these tools are the Laws of Probability. Probability can tell us a lot about a system - for example, in a room filled with gas it is far more probable that the gas is spread evenly rather than being bunched up in one corner. This may seem to be nothing more than common sense, but it has profound implications, especially when the probabilities involved are studied quantitatively. Through the use of this and other tools, statistical mechanics enables physicists to gain fundamental insight into the workings of the macroscopic world.
