Based on the provided sources, here is a brief overview of the physics and applications of phase transitions across macroscopic, nanoscale, and biological systems.

Classical vs. Nanoscale Phase Transitions Phase transitions describe the transformation of matter between distinct physical states (e.g., solid, liquid, gas). Classical thermodynamics explains these transitions through macroscopic properties like latent heat, temperature, and pressure, with sharp boundaries separating phases on a phase diagram. However, at the molecular and nanoscale, statistical mechanics is required. At these tiny scales, the sharp discontinuities of macroscopic phase transitions blur into continuous gradients due to finite-size effects, thermal fluctuations, and the dominance of surface energy over bulk energy. Furthermore, "quantum phase transitions" can occu ...