Maxwell and the normal distribution: A colored story of probability, independence, and tendency toward equilibrium

Citation data:

Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, ISSN: 1355-2198, Vol: 57, Page: 53-65

Publication Year:
Usage 92
Downloads 61
Abstract Views 26
Link-outs 5
Captures 10
Readers 10
Mentions 6
Links 6
Social Media 1
Tweets 1
Repository URL:
Balázs Gyenis
Elsevier BV
Arts and Humanities, Physics and Astronomy
Most Recent Tweet View All Tweets
article description
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 H-theorem. 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.

This article has 6 Wikipedia mentions.

Second law of thermodynamics

The second law of thermodynamics states that the total entropy can only increase over time for an isolated system, meaning a system which neither energy nor matter can enter or leave. The total entropy can remain constant in ideal cases where the system is in a steady state (e...

Read full Article

Maxwell–Boltzmann distribution

In Physics (in particular in statistical mechanics), the Maxwell–Boltzmann distribution is a particular probability distribution named after James Clerk Maxwell and Ludwig Boltzmann. It was first defined and used for describing particle speeds in idealized gases where the part...

Read full Article

Molecular chaos

In the kinetic theory of gases in physics, the molecular chaos hypothesis (also called Stosszahlansatz in the writings of Paul Ehrenfest cite arxiv ) is the assumption that the velocities of colliding particles are uncorrelated, and independent of position. James Clerk Maxwell...

Read full Article

Irreversible process

In science, a process that is not reversible is called irreversible. This concept arises frequently in thermodynamics.In thermodynamics, a change in the thermodynamic state of a system and all of its surroundings cannot be precisely restored to its initial state by infinitesim...

Read full Article

Statistical mechanics

Statistical mechanics is a branch of theoretical physics that uses probability theory to study the average behaviour of a mechanical system, where the state of the system is uncertain.The term statistical mechanics is sometimes used to refer to only statistical thermodynamics....

Read full Article

Kinetic theory of gases

The kinetic theory describes a gas as a large number of submicroscopic particles (atoms or molecules), all of which are in constant rapid motion that has randomness arising from their many collisions with each other and with the walls of the container.Kinetic theory explains m...

Read full Article