  We discuss thermal and active fluctuations of a compressible bilayer vesicle
by using the results of hydrodynamic theory for vesicles. Coupled Langevin
equations for the membrane deformation and the density fields are employed to
calculate the power spectral density matrix of membrane fluctuations. Thermal
contribution is obtained by means of the fluctuation dissipation theorem,
whereas active contribution is calculated from exponentially decaying time
correlation functions of active random forces. We obtain the total power
spectral density as a sum of thermal and active contributions. An apparent
response function is further calculated in order to compare with the recent
microrheology experiment on red blood cells. An enhanced response is predicted
in the low-frequency regime for non-thermal active fluctuations.
