Maxwell and the normal distribution: A colored story of probability, independence, and tendency toward equilibrium
Abstract
We investigate Maxwell's attempt to justify the mathematical assumptions behind his 1860 Proposition IV according to which the velocity components of colliding particles follow the normal distribution. Contrary to the commonly held view we find that his molecular collision model plays a crucial role in reaching this conclusion, and that his model assumptions also permit inference to equalization of mean kinetic energies (temperatures), which is what he intended to prove in his discredited and widely ignored Proposition VI. If we take a charitable reading of his own proof of Proposition VI then it was Maxwell, and not Boltzmann, who gave the first proof of a tendency towards equilibrium, a sort of Htheorem. We also call attention to a potential conflation of notions of probabilistic and value independence in relevant prior works of his contemporaries and of his own, and argue that this conflation might have impacted his adoption of the suspect independence assumption of Proposition IV.
 Publication:

Studies in the History and Philosophy of Modern Physics
 Pub Date:
 February 2017
 DOI:
 10.1016/j.shpsb.2017.01.001
 arXiv:
 arXiv:1702.01411
 Bibcode:
 2017SHPMP..57...53G
 Keywords:

 Maxwell;
 Kinetic theory;
 Statistical mechanics;
 Normal distribution;
 Independence;
 Htheorem;
 Second law of thermodynamics;
 Condition A;
 Physics  History and Philosophy of Physics
 EPrint:
 3 figures