Stellar energy balance equation ($\partial L/\partial m={ϵ}_{\mathrm{nuc}}-{ϵ}_{\nu }-Du/Dt-PD(1/\rho )/Dt$)

For a slowly evolving spherical star, the Lagrangian energy equation separates nuclear rest-mass release, stellar neutrino energy loss, thermal storage and pressure-volume work. Specific internal energy and nuclear energy conventions must avoid counting nuclear mass changes or escaping reaction-neutrino energy twice. At fixed composition the gravothermal stellar energy generation is $-TDS/Dt$. Energy transport processes redistribute heat rather than creating it.

Escaping neutrinos remove energy produced by nuclear reactions or drawn from thermal reservoirs. Pair annihilation, plasma excitations, photoneutrino emission and electron-ion bremsstrahlung provide thermal losses. This reduces photon luminosity or increases the required nuclear and gravothermal supply. At sufficiently extreme collapse densities, neutrino transport must replace a free-escape loss approximation.

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.