The Boltzmann‐Ehrenfest adiabatic invariance formalism used to derive the acoustic radiation stress equation for solids [J. H. Cantrell, Jr., Phys. Rev. B30, 3214 (1984)] is combined with recent developments in stochastic classical dynamics to obtain the internal and Helmholtz free energies in terms of random zero‐point nonlinear acoustic modes. The results lead to an expression of the thermal expansion coefficients of crystalline solids in terms of nonlinearity parameters related directly to the acoustic radiation‐induced static strains. When the model acoustic non‐linearity parameters are set to zero, the internal energy expresionreducesto the Planck radiation law obtained from quantum mechanics. If, in addition, the quasiharmonic assumption is invoked for the model frequencies, the thermal expansion equationreducesto that obtained from Debye‐Grüneisen‐Einstein statistical model of a system of quantum oscillators.