Statistical Mechanics Partition Function

Z(β) and thermodynamic observables for quantum systems

Temperature (kT/ε): 1.00

Number of levels: 8

System:

Z(β)

—

Σ e^{-βEn}

⟨E⟩

—

−∂ln Z/∂β

F = −kT ln Z

—

Helmholtz free energy

S/k

—

β⟨E⟩+ln Z

Cv/k

—

β²(⟨E²⟩−⟨E⟩²)

⟨n⟩ (occ)

—

mean level

Z(β) = Σₙ e^{-βEₙ}, ⟨E⟩ = −∂lnZ/∂β, F = −kT·lnZ, S = (⟨E⟩−F)/T, Cᵥ = ∂⟨E⟩/∂T