Abstract
The article by M. Greenspan on the Boltzmann‐Ehrenfest adiabatic principle [J. Acoust. Soc. Am. 27, 34 (1955)] is used as the starting point for discussing the role of adiabatic invariance (or integrability) in modern physics. These conserved properties of open systems constitute the key concept upon which all advances in modern physics have been focused. These include the origin of thermodynamic irreversibility for Hamiltonian systems and the quantization of motion. Delauney (1860) was first to employ adiabatic invariants as dynamical variables with an aim toward determining the stability of the solar system. This issue eventually culminated in the work by Kolmogorov, Arnold, and Moser on the stability of nearly integrable systems. The solution to the problem of soliton motion by the inverse scattering transformation is in fact a transformation to the adiabatic invariant as the canonical momentum. Recent acoustical applications of adiabatic invariance include a determination of the potential in an acoustic levitator and a prediction of second sound in acoustic turbulence.
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