Warm-Up Exercise 10

Due 1:00 pm, Thu, Sep. 29

Physics 313R, Fall Semester, 2011

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Did you complete the reading assignment?
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You've seen something much like Eq. 6.3 in this class before. Where? And did it work well for what you used it for?

Consider the possible arrangements of placing 9 checkers on the 8x8 grid of a checkerboard. Which of the possible arrangements is least likely? Which has the highest entropy? Explain.

The discussion on page 198 is a lot of effort to generalize something we already have an intuitive feel for. Remember the random walker program where we computed the entropy as a function of time (steps)? What arrangement had the highest entropy? Recall the number of ways of arranging N things in m bins is the binomial, "N choose m," that is N!/(m!(N-m)!). For what value of m is the binomial maximized? Make a plot or something to convince yourself.

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