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. References External links The Fundamental Thermodynamic Relation Thermodynamics Statistical mechanics Thermodynamic equations