⚛️ Gibbs Ensemble (2D)

Discrete energy levels in contact with a heat bath at temperature T. Each particle occupies a level with probability p(E) ∝ e^-E/kT. Adjust T and watch the histogram converge to the Boltzmann curve.

Controls

Temperature kT/ε₀ 1.00 Energy levels L 8 Particles N 300

Ensemble statistics

Partition function Z—

Average energy ⟨E⟩/ε₀—

Entropy S/k—

Free energy F/ε₀—

Heat capacity C/k—

Z = Σᵢ e^-Eᵢ/kT
p(Eᵢ) = e^-Eᵢ/kT / Z
⟨E⟩ = Σᵢ p(Eᵢ)·Eᵢ = -∂(ln Z)/∂β
S/k = -Σᵢ p(Eᵢ)·ln p(Eᵢ)
F = -kT·ln Z = ⟨E⟩ - TS