Gibbs 1902: closed system at fixed T has Boltzmann-distributed states P_i = exp(-E_i/k_BT)/Z where Z = Σ exp(-E_i/k_BT). Helmholtz free energy A = -k_BT ln Z; ⟨E⟩ = -∂ln Z/∂β. Foundation of equilibrium-thermodynamics-from-microstates.
Gibbs 1902: closed system at fixed T has Boltzmann-distributed states P_i = exp(-E_i/k_BT)/Z where Z = Σ exp(-E_i/k_BT). Helmholtz free energy A = -k_BT ln Z; ⟨E⟩ = -∂ln Z/∂β. Foundation of equilibrium-thermodynamics-from-microstates.