# Books in the balance

A system is said to obey detailed balance if every forward process is balanced by its reverse process. In other words, there is no net movement from any state to any other state.

Suppose Sue has 250 books on her shelf, and there are a total of 15,000 books she is potentially interested in buying from booksellers. If Sue's bookshelf is in detailed balance with the world of booksellers, find $\frac{P(\text{book from Sue's shelf}\rightarrow \text{ booksellers})}{P(\text{book from booksellers}\rightarrow \text{ Sue's shelf})}$

Details

• A book might go from Sue's shelf, to the booksellers if Sue sells some of her books to a bookseller, or donates some of them.
• $$P(A\rightarrow B)$$ represents the probability of a book going from state $$A$$ to state $$B$$.
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