Statistical Mechanics: Phase Transitions & Phase Diagrams

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Phase transitions represent qualitative changes in matter, such as the transition from liquid to gas or solid to liquid, marked by sharp boundaries. These transitions are crucial for classifying systems and understanding their behavior. The concept of critical exponents at phase transitions helps identify 'universality' classes, indicating that diverse systems can exhibit similar behaviors. This framework aids in organizing and comprehending various phenomena across different fields. Notably, some discussions suggest surprising connections between seemingly unrelated processes, such as evolution and Bose-Einstein Condensates.
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why phase transitions and points in phase diagrams important?
 
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Phase transitions are qualitative changes (sharp boundaries between different phases) like boiling a liquid into gas, or a solid melting into liquid.
 
Also, its at phase transitions where you can classify systems. I'm just starting to learn about this but the way a phase transition occurs involves the notion of a critical exponent and this can be used to determine 'universality' classes. So very different systems can act exactly the same at a phase transition. Presumably this helps us organize and understand diverse phenomena. For example I saw a talk last fall suggesting that evolution was in the same class as the Bose-Einstein Condensate (if that surprised you it surprised most other folks there as well).
 

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