Entropy & Ideal Gas Mixing
Boltzmann's H-theorem in action: watch entropy rise as two gases mix
S_red: 0.00
S_blue: 0.00
ΔS_mix: 0.00
T_eff: 1.00
Boltzmann entropy S = k_B ln Ω counts accessible microstates. For an ideal gas, entropy increases as the volume accessible to each particle grows.
Mixing entropy: when two gases of equal N mix into double the volume, ΔS_mix = 2Nk_B ln(2) — irreversible even for identical particles (Gibbs paradox).
Particles undergo elastic collisions. Speed distribution approaches Maxwell-Boltzmann as the system thermalizes.
The entropy plot (right) shows entropy rising monotonically after the partition is removed — the statistical arrow of time.