1. How is the notion of an ensemble connected with the "fundamental assumption" of thermal physics? (To answer this, you might consider expressing the fundamental assumption in your own words, explaining what an ensemble is, and then linking those two explanations.)
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2. Suppose the two binary spin systems S1 and S2 are put in thermal contact with one another. Estimate their most probable configuration once they have reached thermal equilibrium. (You might want to express this in terms of how many spin up and spin down sites each system will possess when the systems reach thermal equilibrium.) If this question seems confusing to you, please specify what you do and don't understand.
3. Consider two large systems which can be characterized by values s1 and s2. (We can think of these as being half the "spin excess" of the systems if we wish, but they could also be other parameters that characterize the systems.) A "configuration" of the combined system is defined to be the set of all states with the specified s1 and s2values. Which of the following is/are correct?
Check the correct answer: a) An accurate average of a physically measurable parameter of the system can be determined by averaging over only the most probable configuration. b) The statistical properties of the combined system must be determined by averaging over all configurations. c) The multiplicity function for the combined system is very sharply peaked about its most probable configuration value. d) Choices (a) and (b). e) Choices (a) and (c). f) None of the above.
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