Adiabatic invariance and its application to Wien's complete displacement law of blackbody radiation.

The article focuses on deriving the complete (or strong) version of Wien's displacement law using the algebra of adiabatic invariants, linking thermodynamic systems composed of finite frequency intervals of blackbody radiation with the dynamics of individual electromagnetic waves. It clarifies the distinction between the complete and partial (or weak) forms of Wien's displacement law, emphasizing the original meaning related to the entire blackbody spectrum rather than just the peak frequency. The derivation employs classical thermodynamics and wave dynamics, extending the approach to analogous displacement laws for classical ideal gases and phonons in the Debye model of solids. This method highlights the role of adiabatic invariance in constraining spectral energy distributions across different physical systems without relying on quantum assumptions.