In an adiabatically shielded system the total enthalpy is conserved. Enthalpy fluctuations of an arbitrarily chosen subsystem must be buffered by the remainder of the total system which serves as a heat reservoir. The magnitude of these fluctuations depends on the size of the reservoir. This leads to various interesting consequences for the physical behavior of the subsystem. As an example, we treat a lipid membrane with a phase transition that is embedded in an aqueous reservoir. We find that large fluctuations are attenuated when the reservoir has finite size. This has consequences for the compressibility of the membrane since volume and area fluctuations are also attenuated. We compare the equilibrium fluctuations of subsystems in finite reservoirs with those in periodically driven systems. In such systems, the subsystem has only finite time available to exchange heat with the surrounding medium. A larger frequency therefore reduces the volume of the accessible heat reservoir. Consequently, the fluctuations of the subsystem display a frequency dependence. While this work is of particular interest for a subsystem displaying a transition such as a lipid membrane, some of the results are of a generic nature and may contribute to a better understanding of relaxation processes in general.