Energy landscapes for cooperative processes: nearly ideal glass transitions, liquid-liquid transitions and folding transitions.

We describe basic phenomenology in the physics of supercooling liquids at constant volume (most simulations), and at constant pressure (most laboratory experiments) before focusing attention on the exceptional cases that exhibit liquid-liquid phase transitions on constant-pressure cooling. We give evidence for point defects in glasses and liquids near T(g). Models based on defects predict transitions with density gaps in constant-pressure systems. We describe the energy landscape representation of such systems. Water, in these terms, is post-critical, and its nearly ideal glass formation can be related to nucleation-free protein 'funnel-folding'. For nucleated folding of proteins, a pseudo-gap should be present. Experimental methods of distinguishing between alternative folding scenarios are described.