By Robert H. Swendsen

This article offers the 2 complementary facets of thermal physics as an built-in conception of the homes of topic. Conceptual realizing is promoted by way of thorough improvement of easy suggestions. not like many texts, statistical mechanics, together with dialogue of the necessary likelihood concept, is gifted first. this gives a statistical starting place for the concept that of entropy, that is relevant to thermal physics. a special function of the ebook is the advance of entropy in response to Boltzmann's 1877 definition; this avoids contradictions or advert hoc corrections present in different texts. certain basics offer a average grounding for complex themes, similar to black-body radiation and quantum gases. an in depth set of difficulties (solutions can be found for teachers throughout the OUP website), many together with specific computations, strengthen the center content material through probing crucial recommendations. The textual content is designed for a two-semester undergraduate direction yet may be tailored for one-semester classes emphasizing both element of thermal physics. it's also appropriate for graduate study.

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4 Probability Theory Because of the importance of probability theory in statistical mechanics, two chapters are devoted to the topic. The chapters discuss the basic principles of the probability theory of discrete random variables (Chapter 3) and continuous random variables (Chapter 5). The mathematical treatment of probability theory has been separated from the physical application for several reasons: (1) it provides an easy reference for the mathematics, (2) it makes the derivation of the entropy more compact, and (3) it is unobtrusive for those readers who are already completely familiar with probability theory.

47) in an approximate but highly accurate form. P (n|N ) = N! (N − n)! 76) + n ln p + (N − n) ln(1 − p) Note that the contributions from the second term in Stirling’s approximation in eq. 74) cancel in eq. 76). Using Stirling’s approximation to the binomial distribution turns out to have a number of pleasant features. We know that the binomial distribution will be peaked, and that its relative width will be small. We can use Stirling’s approximation to ﬁnd the location of the peak by treating n as a continuous variable and setting the derivative of the logarithm of the probability distribution with respect to n in eq.

All three deﬁnitions of probability have the same mathematical structure. This reduces the amount of mathematics that we have to learn, but unfortunately does not resolve the controversies. 2) and assigning a probability P (aj ) to each event. The combination of random events and their probabilities is called a ‘random variable’. If the number of elementary events is a ﬁnite or countable, it is called a ‘discrete random variable’. 3) for all aj . An impossible event has probability zero, and a certain event has probability 1.