  We present a unified approach to thermodynamic description of one, two and
three dimensional phases and phase transformations among them. The approach is
based on a rigorous definition of a phase applicable to thermodynamic systems
of any dimensionality. Within this approach, the same thermodynamic formalism
can be applied for the description of phase transformations in bulk systems,
interfaces, and line defects separating interface phases. For both lines and
interfaces, we rigorously derive an adsorption equation, the phase coexistence
equations, and other thermodynamic relations expressed in terms of generalized
line and interface excess quantities. As a generalization of the Gibbs phase
rule for bulk phases, we derive phase rules for lines and interfaces and
predict the maximum number of phases than may coexist in systems of the
respective dimensionality.
