In this paper Boltzmann Machines, the first paragraph of the second section 2. Boltzmann Machines argues that,
we could never train such a network with three units to visit the states (0,0,0), (0,1,1), (1,0,1) and (1,1,0) with some probabilities, but not the other four possible states. This is because the first and second order statistics (the mean of each component and correlations between components) are the same for these four states as the remaining four and so the network can not discriminate them.
As I learned from here, order logic is just to order the attributes of the samples and take the i-th element of it.
I am wondering why the first and second order statistics of the two sets are the same.