The active transfer of phospholipids between membrane leaflets (flip-flop), mediated by (adenosine triphosphate) ATP-dependent enzymes such as flippases and floppases, is a key regulator of membrane asymmetry and curvature. However, the theoretical understanding of curvature generation driven by flip-flop under external perturbations remains incomplete. Here we present a mesoscopic thermodynamic model in which lipid asymmetry couples to membrane curvature via a Landau-type free energy, with curvature as the order parameter and transmembrane voltage as the control parameter. This framework predicts an electrically driven phase transition analogous to a ferroelectric transition. The model reproduces field-induced bistability, critical susceptibility divergence, and hysteresis, with numerical simulations revealing thickness-dependent curvature thresholds and robust curvature-memory effects. These results clarify how electric-field-driven lipid redistribution governs membrane shape and suggest strategies for voltage-controlled nanoscale memory and shape encoding.

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• Bending
• Capacitance
• Charge
• Dielectric properties
• Diffusion
• Electric field alignment
• Electric field effects
• Electric polarization
• Electrical properties of membranes
• Electrochemical properties
• Ferroelectric phase transition
• Ferroelectricity
• Ferroelectrics
• Flexoelectricity
• Landau levels
• Landau theory
• Mathematical physics
• Mechanisms of phase transition regulation & control in biology
• Mechanobiology
• Membrane fluctuations
• Membranes
• Order parameters
• Phase diagrams
• Phase transitions in biological systems
• Phase transitions in cellular systems
• Protein dynamics, structure & function
• Thermodynamics
• Lipids
• Landau-Ginzburg-Devonshire theory