1. M. Planck.Ann. Phys. (Leipzig) 1, 69 122 (1900).
2. There is a quantum field analogue of this problem. Malament (unpublished) considered a free quantum field in the vacuum state and two detectors located in separate positions in space. (A detector is just a system with two distinct states, “ground state” and “exited state”.) He proved that if one detector jumps to the exited state then the probability that the second detector will also do so increases, despite the spacelike separation between the two events. This type of nonlocalily should be distinguished from the (stronger) notion of J. Bell.Physics 1, 195 200 (1964). On the subject of nonlocalily in quantum field theory, see M. Redhead.Found. Phys. 25, 123 137 (1995), and references therein!
3. See. for example. Y. S. Chow, and H. Teicher.Probability Theory: Independence, Interchangeability. Martingales (Springer. New York. 1978), p. 186.
4. The derivations of the distribution from maximum entropy considerations fall in the second category. It can be shown that taking maximum entropy is equivalent to assuming total factorizability of the distribution function.
5. L. D. Landau, and E. M. Lifshitz,Statistical Physics. Part 1, 3rd edn. (Pergamon, Oxford. 1980). p. 7.