Perturbative inflaton reheating equations (${\dot{\rho }}_{\varphi }+3H{\rho }_{\varphi }=-\Gamma {\rho }_{\varphi },{\dot{\rho }}_r+4H{\rho }_r=\Gamma {\rho }_{\varphi }$)

A coarse-grained description in which quadratic inflaton oscillations have zero mean pressure and lose energy at constant effective decay rate $\Gamma$ to a relativistic component. Adding the equations preserves total energy accounting with the appropriate expansion work. Efficient transfer occurs around $H\sim \Gamma$, but producing particles and achieving thermal equilibrium are different steps. The potential alone does not specify the decay rate or thermalization interactions.