The Entropic Concavity Framework: A Universal Formulation for Understanding Phase Transitions

A unifying description of phase transitions is proposed, based only on the notion of Boltzmann entropy, or equivalently, the density of states function and Jaynes's Maximum Entropy Principle. Being a universal description, it can be applied to systems from both traditional physics, such as of interacting particles of arbitrary composition and interaction ranges, and more general systems of interconnected variables, e.g. networks, combinatorial structures, biological systems, etc. We demonstrate that this approach recovers the key properties of phase transitions and yields a rigorous classification of their nature in both physics and non-physics type systems. We present several examples such as the two-star model, Strauss' cluster model of transitive networks, gelation in random graphs (Erdös–Rényi), magnetic spin models with short range interactions such as the Ising model, the Blume--Emery--Griffiths model, which is characterized by long-range interactions and finally, the Van der Waals gas as a model system with continuous variables.