Frame tension governs the thermal fluctuations of a fluid membrane: new evidence

Two different tensions can be defined for a fluid membrane: the internal tension, gamma, conjugated to the real membrane area in the Hamiltonian, and the frame tension, tau, conjugated to the projected (or frame) area. According to the standard statistical description of a membrane, the fluctuation spectrum is governed by gamma. However, using rotational invariance arguments, several studies argued that the fluctuation spectrum must be governed by the frame tension tau instead. These studies disagree on the origin of the result obtained with the standard description yet: either a miscounting of configurations, quantified with the integration measure, or the use of a quadratic approximation of the Helfrich Hamiltonian. Analyzing the simplest case of a one-dimensional membrane, for which the arc length offers a natural parametrization, we give a new proof that the fluctuations are driven by tau, and show that the origin of the issue with the standard description is a miscounting of membrane configurations. The origin itself of this miscounting depends on the thermodynamic ensemble in which calculations are made.

Automated summary

This study provides a new proof that the fluctuations of a membrane are driven by the frame tension, and identifies a miscounting of membrane configurations as the origin of the issue with the standard description.