= Solution
The <hot-Jupiter radius inflation> problem is that some strongly irradiated giant planets have radii much larger than standard age-, mass- and composition-dependent cooling models predict. Greater internal <entropy> generally means a larger radius at fixed mass. The two broad classes of explanation are \b[retaining existing heat by delaying cooling] and \b[depositing additional energy into the deep planet].
For <delayed cooling of an inflated giant planet>:
* \b[Enhanced atmospheric <opacity>] slows radiative leakage and keeps the deep interior hot. Required enrichment or persistent cloud <opacity> must be compatible with composition and spectra; adding heavy material also tends to increase density. Insulation can preserve initial heat but cannot necessarily reinflate an already cooled planet.
* \b[<Layered convection in a giant planet>] uses a stabilizing composition gradient and double-diffusive layers to reduce heat transport. The needed gradient and layer structure must survive mixing, and their efficiency is model-dependent; very inefficient transport cannot simply be assumed for every planet.
For <heating of an inflated giant planet>:
* \b[<Tidal heating>] dissipates orbital or spin energy, often requiring maintained eccentricity or obliquity. Nearly circular, synchronized planets have little of the simplest eccentricity-tide power, so a pumping mechanism or different tidal configuration is needed to explain them.
* \b[<Ohmic heating of a giant planet>] dissipates wind-induced electric currents in a conducting, magnetized atmosphere and interior. It requires appropriate ionization, conductivity, magnetic field, wind speeds and sufficiently deep deposition; magnetic drag can limit the available mechanical power.
Surface or upper-atmosphere heating that is promptly reradiated need not raise deep <entropy>. The depth and long-term power budget distinguish an effective inflation mechanism from one that merely changes a photospheric temperature.
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