  Luminescent solar concentrators (LSCs) are theoretically able to concentrate
both direct and diffuse solar radiation with extremely high efficiencies.
Photon-multiplier luminescent solar concentrators (PM-LSCs) contain
chromophores which exceed 100\% photoluminescence quantum efficiency. PM-LSCs
have recently been experimentally demonstrated and hold promise to outcompete
traditional LSCs. However, we find that the thermodynamic limits of PM-LSCs are
different and are sometimes more extreme relative to traditional LSCs. As might
be expected, to achieve very high concentration factors a PM-LSC design must
also include a free energy change, analogous to the Stokes shift in traditional
LSCs. Notably, unlike LSCs, the maximum concentration ratio of a PM-LSC is
dependent on brightness of the incident photon field. For some brightnesses,
but equivalent energy loss, the PM-LSC has a greater maximum concentration
factor than that of the traditional LSC. We find that the thermodynamic
requirements to achieve highly concentrating PM-LSCs differ from traditional
LSCs. The new model gives insight into the limits of concentration of PM-LSCs
and may be used to extract design rules for further PM-LSC design.
