Gravitational Waves as Thermodynamic Shear Excitations in Scalar-Tensor Gravity

In Jordan-frame scalar--tensor gravity, a timelike scalar gradient defines an effective thermodynamic medium. We show that a transverse--traceless perturbation of a homogeneous shear-free background activates the local shear-work channel $\mathcal W_\phi=\pi_{ab}^{(\phi)}\sigma^{ab}$, with leading pure-TT contribution $\mathcal P_{\rm TT}^{[1,1]} =\overline{\mathcal K\mathcal T} \dot\chi_{ij}^{\rm TT}\dot\chi_{\rm TT}^{ij}/4$. This stress power follows from local traction mechanics, enters the scalar-sector energy balance, and is gauge invariant at second order. The same scalar--tensor coupling controls non-GR tensor damping and appears with the opposite sign in a GR-normalized amplitude balance, although its interpretation as a separate tensor-energy source is normalization dependent. Scalar--tensor gravity thus provides a controlled example in which a propagating spin-2 mode acquires an intrinsically gravitational thermodynamic interpretation.