Passages and droplets in lamellar fluid membrane phases

We consider thermally excited passages and droplets formed between fluid membranes in a lamellar phase. We show that they induce entropic attractive interactions which compete with Helfrich's entropic intermembrane repulsion. This competition determines the intermembrane distance lₘₐₓ lamellar phases reach at transitions to isotropic fluid membrane phases. In general, lₘₐₓ is much smaller than the membrane persistence length and crucially depends on membrane saddle-splay (``Gaussian'') rigidity.