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4. The Interpretation of Statistical Quantities — Introduction to Statistical Mechanics

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In Chapter 2 I defined lots of quantities, but said very little about what they really mean. Now it is time to return to them. We will study them in more detail and try to build up an intuitive understanding of what they represent. Temperature is a quantity we are all familiar with. You have probably been told that it measures the microscopic jiggling of atoms: the faster they are moving, the hotter an object feels. So when I defined it in terms of a derivative of the density of states, a seemingly unrelated concept, you were probably a little surprised. To resolve this seeming paradox, I am going to prove a very important theorem called the equipartition theorem. Once you reach the end, the significance of temperature will become clear. In general, the energy of a system can depend in an arbitrary way on all of its microscopic variables, which we will call x 1 x1 , x 2 x2 , etc. That is, the energy is a function E( x 1 , x 2 ,…) E(x1,x2,…) . But there are some very important specia

4. The Interpretation of Statistical Quantities - Introduction to Statistical Mechanics Navigation index next | previous | Introduction to Statistical Mechanics >> 4. The Interpretation of Statistical Quantities ¶ In Chapter 2 I defined lots of quantities, but said very little about what they really mean. Now it is time to return to them. We will study them in more detail and try to build up an intuitive understanding of what they represent. 4.1. Temperature ¶ Temperature is a quantity we are all familiar with. You have probably been told that it measures the microscopic jiggling of atoms: the

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