Unnormalized probability: A different view of statistical mechanics
All teachers and students of physics have absorbed the doctrine that probability must be normalized. Nevertheless, there are problems for which the normalization factor only gets in the way. An important example of this counter-intuitive assertion is provided by the derivation of the thermodynamic entropy from the principles of statistical mechanics. Unnormalized probabilities provide a surprisingly effective teaching tool that can make it easier to explain to students the essential concept of entropy. The elimination of the normalization factor offers simpler equations for thermodynamic equilibrium in statistical mechanics, which then lead naturally to a new and simpler definition of the entropy in thermodynamics. Notably, this definition does not change the formal expression of the entropy based on composite systems that I have previously offered. My previous definition of entropy has been criticized by Dieks, based on what appears to be a misinterpretation. I believe that the new definition presented here has the advantage of greatly reducing the possibility of such a misunderstanding—either by students or by experts.