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Gibbs Phase Rule describes the nature of phase boundaries on phase diagrams, and is a foundational principle in materials thermodynamics. In Gibbs original derivation, he stipulates that the Phase Rule applies only to simple systems--defined to be homogeneous, isotropic, uncharged, and large enough that surface effects can be neglected; and not acted upon by electric, magnetic or gravitational fields. Modern functional materials; spanning nanomaterials, multiferrorics, materials for energy storage and conversion, colloidal crystals, etc.; are decidedly non-simple, leveraging various additional forms of thermodynamic work to achieve their functionality. Here, we extend Gibbs original arguments on phase coexistence to derive a generalized Phase Rule, based in the combinatorial geometry of high-dimensional convex polytopes. The generalized Phase Rule offers a conceptual and mathematical framework to interpret equilibrium and phase coexistence in advanced modern materials.
We review some recent developments in the study of Gibbs and non-Gibbs properties of transformed n-vector lattice and mean-field models under various transformations. Also, some new results for the loss and recovery of the Gibbs property of planar ro
We consider the problem of approximate sampling from the finite volume Gibbs measure with a general pair interaction. We exhibit a parallel dynamics (Probabilistic Cellular Automaton) which efficiently implements the sampling. In this dynamics the pr
The concept of generalized Gibbs ensembles (GGEs) has been introduced to describe steady states of integrable models. Recent advances show that GGEs can also be stabilized in nearly integrable quantum systems when driven by external fields and open.
We derive a class of equations of state for a multi-phase thermodynamic system associated with a finite set of order parameters that satisfy an integrable system of hydrodynamic type. As particular examples, we discuss one-phase systems such as the v
In this paper, we study the diffusive limit of solutions to the generalized Langevin equation (GLE) in a periodic potential. Under the assumption of quasi-Markovianity, we obtain sharp longtime equilibration estimates for the GLE using techniques fro