Fluctuations of systems in finite heat reservoirs with applications to phase transitions in lipid membranes

摘要

In an adiabatically shielded system the total enthalpy is conserved. Enthalpyfluctuations of an arbitrarily chosen subsystem must be buffered by theremainder of the total system which serves as a heat reservoir. The magnitudeof these fluctuations depends on the size of the reservoir. This leads tovarious interesting consequences for the physical behavior of the subsystem. Asan example, we treat a lipid membrane with a phase transition that is embeddedin an aqueous reservoir. We find that large fluctuations are attenuated whenthe reservoir has finite size. This has consequences for the compressibility ofthe membrane since volume and area fluctuations are also attenuated. We comparethe equilibrium fluctuations of subsystems in finite reservoirs with those inperiodically driven systems. In such systems, the subsystem has only finitetime available to exchange heat with the surrounding medium. A larger frequencytherefore reduces the volume of the accessible heat reservoir. Consequently,the fluctuations of the subsystem display a frequency dependence. While thiswork is of particular interest for a subsystem displaying a transition such asa lipid membrane, some of the results are of a generic nature and maycontribute to a better understanding of relaxation processes in general.