Boltzmann's H-theorem — irreversible mixing and entropy increase
Gas Chamber
Entropy vs Time
S = 0.00 (0% of max)
Blue left: 100%
Blue particles start left, red right. Remove the wall to watch irreversible mixing.
Shannon entropy S = -Σ pᵢ log(pᵢ) over spatial bins increases toward maximum.
The H-theorem (Boltzmann 1872): H can only decrease or stay constant — equivalent to entropy non-decrease.
Reversibility paradox: microscopic laws are time-symmetric, yet macroscopic mixing is irreversible.