Phase transitions are an incredibly important area of physics. Physicists take two different approaches to phase transitions. On the one hand, we can treat each phase as its own statistical mechanical system.

Figure 1: The chemical potential of a solid liquid and gas. The lowest chemical potential is the equilibrium phase. Where the chemical potentials cross is the phase transition.

Second order transitions. In a second-order phase transition the first derivatives of G vanish and the Clapeyron equation is replaced by a condition involving second derivatives.

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In physics, phase space is a concept which unifies classical (Hamiltonian) mechanics and quantum mechanics; in mathematics, phase space is a concept which unifies symplectic geometry with …

A phase transition is an abrupt, discontinuous change in the properties of a system. We’ve already seen one example of a phase transition in our discussion of Bose-Einstein condensation.

Based on the definition of a phase in Ch. 1a, a phase transformation occurs when one or more phases in a material change their chemical or physical (incl. structural) properties upon a change of the …