Using the probability for the state of k non-contiguous sites of equation 6.35 we find that the entropy of these sites is given by
In the thermodynamic limit (
) and using the substitution of equations 6.21 and 6.22 we find that the entropy per spin is given by
Compare equation 6.37 to equation 6.24. If the spins are equally spaced, and we let the spacing be 
, 
, and define 
to be the entropy per spin of an infinite ising system, taking every dth spin, while 
is the similar quantity, but for k of the spins with the spacing d, then
In zero external field, where from equation 6.27 the eigenvector components have values 
, this becomes
which should be compared with equation 6.30. Probabilities of same and different spins separated by d are also similarly given (see equation 6.29) by
