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We develop a theoretical framework to quantify how active forces renormalize the effective bending rigidity, Gaussian modulus, and surface tension of thermally fluctuating membranes. Building on classical statistical mechanics, we extend the analysis to include nonequilibrium active forces, both direct forces and those coupled to membrane curvature, within a nonlinear continuum formulation. Our model also incorporates hydrodynamic interactions mediated by the surrounding viscous fluid, which significantly alter the fluctuation spectrum. We find that direct active forces enhance long-wavelength undulations, leading to a substantial reduction in both the effective bending rigidity and surface tension, with the extent of softening strongly modulated by fluid viscosity. In contrast, curvature-coupled active forces primarily influence intermediate and short-wavelength fluctuations and show minimal sensitivity to viscosity. Together, these findings provide key insights into the nonequilibrium mechanics of active membranes and yield testable predictions for interpreting fluctuation spectra in both biological contexts and engineered membrane systems. 

Entropic pressure, a longstanding topic of interest in biophysics and biomechanics, has been studied for over four decades. Similar to an ideal gas, fluctuating surfaces can generate entropic pressure through thermally driven motions. These thermal fluctuations impact a wide range of biological activities, including but not limited to vesicle fusion, cell adhesion, exocytocis, and endocytocis among many others. It has been proposed (and validated) by many researchers that the entropic pressure near a fluctuating confined fluid membrane without surface tension scales as p∝1/d3, where d is the confining distance, and this power law is size independent. In this article, we show that entropic pressure near a fluctuating fluid membrane could be strongly affected by the membrane’s size and surface tension. We show that while for membranes of size L=1μm and larger, the pressure is size independent, for smaller membranes, the pressure does indeed depend on the membrane’s size. Our findings also shows that the surface tension changes this scaling law and at larger distance makes the pressure decay exponentially. Our work provides insights into how surface tension enhances biological vesicles fusion by suppressing membrane fluctuations, and consequently, the repulsive entropic force, and impacts biomembranes interactions with external objects at the early stage of approaching.