What is a phase transition, and why does change come suddenly?

A phase transition is a drastic change between thermodynamic phases that occurs as parameters such as temperature and pressure are varied. Melting ice near 0°C at 1 atm is the familiar example. The change is sudden because the stable phase is the one with the lowest free energy, and a smooth change in conditions can make a different phase the lowest. Free energy balances an ordering tendency from energy against a disordering tendency from entropy. [1] [2]

A phase is characterized by a thermodynamic function, typically the free energy, which depends on a few macroscopic parameters. A phase diagram plots those parameters on its axes and marks which phase applies at each point. Phase boundaries separate phases, and crossing one produces a sudden change. A boundary can end at a critical point, where the two phases become indistinguishable and the substance behaves anomalously. A triple point is another feature of a typical diagram. [1]

One lecture source puts it as a smooth change in pressure or temperature causing an abrupt change in the properties of water when a boundary is crossed. Another defines a transition as a macroscopic rearrangement of a system's internal constituents in response to changed conditions. [3] [4]

The free energy is F = E − TS. The energy term favors order and the entropy term favors disorder. At very low temperature energy dominates, so the ordered solid is most stable. As temperature rises, entropy matters more, and the system moves to the liquid and then the gas. In water's solid phase, molecules sit in a crystal held by hydrogen bonds, giving low energy and low entropy. The liquid has higher energy and entropy, and the gas higher still. [2]

At the melting temperature the free energies of solid and liquid are equal. Extra heat then goes into converting solid to liquid while the temperature stays constant. That extra heat is the latent heat, and observing a latent heat is a sure sign of a phase transition, according to the same source. [2]

Theoretically, the drastic change appears as singularities, or non-analyticities, in quantities such as entropy, volume and specific heat. These can be a jump, a cusp or a divergence. Entropy jumps when ice melts, and volume changes discontinuously when water boils. Transitions with jumps of this kind are labeled first-order, and others are second-order. [1]

Pressure matters most for gases, which are very compressible, while solids and liquids are dense and nearly incompressible. So the solid-liquid line on water's phase diagram is close to vertical. Raising the pressure on a gas shrinks the free energy difference between gas and liquid until it reaches zero, which is the critical point. [2]

Symmetry offers another explanation. A crystal has translational and rotational symmetries that liquids and gases lack, so no continuous path can turn one into the other. This is the Landau symmetry principle: phases with different symmetry groups must always be separated by a transition. Liquid and gas share the same symmetry group, so a path around the critical point can change one into the other continuously. The source also notes that water has at least 15 solid phases, and its account is simplified. [2]