Gravothermal stellar energy generation (${ϵ}_{\mathrm{grav}}=-Du/Dt-PD(1/\rho )/Dt$)

This term accounts for thermal storage and compression or expansion in the stellar energy balance equation. At fixed composition the first law of thermodynamics makes it $-TDS/Dt$. Kelvin-Helmholtz contraction can supply positive luminosity, while thermal adjustment may locally absorb energy. It is not simply the full change in gravitational potential energy: the stellar virial theorem also requires changes in internal energy.