text: It has been shown that the fundamental thermodynamic relation together with the following three postulates
  is sufficient to build the theory of statistical mechanics without the equal a priori probability postulate.
  For example, in order to derive the Boltzmann distribution, we assume the probability density of microstate  satisfies . The normalization factor (partition function) is therefore
  The entropy is therefore given by
  If we change the temperature  by  while keeping the volume of the system constant, the change of entropy satisfies
  where
  Considering that
  we have
  From the fundamental thermodynamic relation, we have
  Since we kept  constant when perturbing , we have . Combining the equations above, we have
  Physics laws should be universal, i.e., the above equation must hold for arbitrary systems, and the only way for this to happen is
  That is
  It has been shown that the third postulate in the above formalism can be replaced by the following:
  However, the mathematical derivation will be much more complicated.