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Unformatted text preview: 7 Statistical Mechanics Statistical mechanics is the study of how macroscopic properties can be derived in terms of detailed microscopic properties. For chemists, statistical mechanics involves understand the macroscopic laws of thermodynamics in terms of Newtons classical laws of atomic motion or quantum mechanics. 7.1 Probability Statistical mechanics focusses on averaging and reducing many microscopic degrees of freedom into fewer macroscopic variables, so that combinatorial math and probability are particularly important. Some of these mathematical tools are described below. Consider two independent events, A and B , which occur with probabilities P ( A ) and P ( B ) respectively. The probability that both events occur is P ( A and B ) = P ( AB ) = P ( A ) P ( B ) (7.1) If these event are exclusive, so that P ( A and B ) = 0, the probability that either event occurs is P ( A or B ) = P ( A ) + P ( B ) . (7.2) If the events are correlated, so that they are not independent or exclusive, it is still possible to determine joint probabilities. The probability that event A occurs given that event B has occurred is P ( A given B ) = P ( A | B ) = P ( A and B ) /P ( B ) . (7.3) For independent events, the probability that A occurs is unaffected by the information...
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