Boltzmann Entropy S = k·ln(Ω) — Microcanonical Ensemble

N = 10 E = 5.0 Ω = — S/k = — T = —

Particles N: 10
Energy E: 5.0
Show: S vs E Ω vs E Phase Space Density Animate Energy Reset

Boltzmann entropy S = k·ln(Ω(E,N)) counts accessible microstates Ω for N ideal gas particles at energy E. The concave S(E) curve ensures positive temperature T = (∂S/∂E)⁻¹.