Model-free thermodynamics of fluid vesicles

Motivated by a long-standing debate concerning the nature and interrelations of surface-tension variables in fluid membranes, we reformulate the thermodynamics of a membrane vesicle as a generic two-dimensional finite system enclosing a three-dimensional volume. The formulation is shown to require two tension variables, conjugate to the intensive constraints of area per molecule and volume-to-area ratio. We obtain the relation between these two variables in various scenarios, as well as their correspondence to other definitions of tension variables for membranes. Several controversies related to membrane tension are thereby resolved on a model-free thermodynamic level. The thermodynamic formulation may be useful also for treating large-scale properties of vesicles that are insensitive to the membrane's detailed statistical mechanics and interactions.