  However, it should be noticed that the assumption that the total energy can be expressed in the form \(E = \sum_i n_i\epsilon_i\) means that the energy of each particle depends only on the cell in which it is located, and not the state of other particles. This can only be maintained, independently of the number \(N\), if there is no interaction at all between the particles. The validity of the argument is thus really restricted to ideal gases.