We present a system exhibiting giant proximity effects which parallel observations in superfluid helium (Perron et al, Nature Physics V. 6, 499 (2010)) and give a theoretical explanation of these phenomena based on the mesoscopic picture of phase coe
xistence in finite systems. Our theory is confirmed by MC simulation studies. Our work demonstrates that such action-at-a-distance can occur in classical systems involving simple or complex fluids, such as colloid-polymer mixtures, or ferromagnets.
