Solving for the Maxwell-Boltzmann Distribution Using Scaling Part 2
Abstract
In Part 1, we argued that one may obtain the Maxwell-Boltzmann distribution p(e) = C(T) exp(-e/T) through scaling arguments if one makes the approximation that e may range from 0 to infinite. We obtained a differential-integral equation and used p(ei) = C(T) exp(-e/T) as a trial solution which solved the problem. Here we solve the problem directly without resort to a trial solution..
Fields of Study & Subjects
Lattice Boltzmann Simulation Studies
Electrostatics and Colloid Interactions
Statistical Mechanics and Entropy
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 2 January 2026
- Document type
- Preprint