First and second order phase transitions differ primarily in the continuity of their thermodynamic properties. First order transitions, like the melting of ice, involve discontinuities in the first derivatives of Gibbs potential and release latent heat, while second order transitions, such as superconductivity, have continuous first derivatives but discontinuous second derivatives. Glass is debated as a second order transition example due to its non-equilibrium nature. The van der Waals gas transition is a classic example of a first order transition, where the free energy's first derivative is discontinuous. Understanding these transitions often involves examining symmetry changes and the behavior of free energy derivatives.
