Physics
Verify that the quantity (k/N)Inr, where In,) is equal to the (mean) entropy of the given system. Show that this leads to essentially the same result for In T if we take, in the foregoing summation, only the largest term of the sum, namely the term Wint) that corresponds to the most probable distribution set. ISurprised? Well, note the following example: For all N, the summation over the binomial coefficients N!/Ir! (N-r!)l gives CNG, 2 r-0 therefore nCNIn2. Now, the largest term in this sum corresponds to r N/2; so, for large N, the logarithm of the largest term is very nearly equal to In(N!)-2In((N/2)!) N, N which agrees with (a).J