V(x) = ½kx² + λx⁴ — energy levels, thermal expansion, Grüneisen parameter
The quartic anharmonicity λx⁴ breaks symmetry when combined with a cubic term (Morse-like), causing thermal expansion: ⟨x⟩_T ≠ 0. The Grüneisen parameter γ = −∂ln ω/∂ln V measures frequency-volume coupling and drives thermal expansion in solids. Anharmonicity also generates phonon-phonon scattering, limiting thermal conductivity in crystals.