Why the Maxwellian Distribution is the Attractive Fixed Point of the   Boltzmann Equation
  The origin of the Boltzmann factor is revisited. An alternative derivation from the microcanonical picture is given. The Maxwellian distribution in a mono-dimensional ideal gas is obtained by following this insight. Other possible applications, as for instance the obtaining of the wealth distribution in the human society, are suggested in the remarks. 
Ricardo Lopez-Ruiz and Xavier Calbet