Related papers: The geometry of high-dimensional phase diagrams: I…
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…
Modern materials are often synthesized or operated in complex chemical environments, where there can be numerous elemental species, competing phases, and reaction pathways. When analyzing reactions using the Gibbs free energy, which has a…
For a multi-component system, general formulas are derived for the dimension of a coexisting region in the phase diagram in various state spaces.
Designing thermodynamic conditions to improve (or reduce) the stability of a target material is a key task in materials engineering. For example, during materials synthesis one aims to enhance the stability of a target phase relative to its…
Gibbs' phase rule states that two-phase coexistence of a single-component system, characterized by an n-dimensional parameter-space, may occur in an n-1-dimensional region. For example, the two equilibrium phases of the Ising model coexist…
Phase separation routinely occurs in both living and synthetic systems. These phases are often complex and distinguished by features including crystallinity, nematic order, and a host of other nonconserved order parameters. For systems at…
We review connections between phase transitions in high-dimensional combinatorial geometry and phase transitions occurring in modern high-dimensional data analysis and signal processing. In data analysis, such transitions arise as abrupt…
Using a minimal algebraic model for the thermodynamics of binary rod--polymer mixtures, we provide evidence for a quintuple phase equilibrium; an observation that seems to be at odds with the Gibbs phase rule for two-component systems. Our…
For different phases to coexist in equilibrium at constant temperature $T$ and pressure $P$, the condition of equal chemical potential $\mu$ must be satisfied. This condition dictates that, for a single-component system, the maximum number…
One of the most fundamental questions we can ask about a given gauge theory is its phase diagram. In the standard model, we observe three fundamentally different types of behavior: QCD is in a confined phase at zero temperature, while the…
The generalized Langevin equation is widely used to model the influence of a heat bath upon a reactive system. This equation will here be studied from a geometric point of view. A dynamical phase space that represents all possible states of…
In an open system, the geometric phase should be described by a distribution. We show that a geometric phase distribution for open system dynamics is in general ambiguous, but the imposition of reasonable physical constraints on the…
The phase coexistence is illuminated with geometric views of the thermodynamic variables, according to Gibbs' choices. Quantities and relations between them are obtained. The existence of the edge of regression with tangents coincident with…
A relativistic mean-field model of nuclear matter with arbitrary proton fraction is studied at finite temperature. An analysis is performed of the liquid-gas phase transition in a system with two conserved charges (baryon number and…
We determine the phase diagram of mixtures of spherical colloids and neutral nonadsorbing polymers in the thermal crossover region between the $\theta$ point and the good-solvent regime. We use the generalized free-volume theory (GFVT),…
Geometrical constructions, such as the tangent construction on the molar free energy for determining whether a particular composition of a solution, is stable, are related to similar tangent constructions on the orientation-dependent…
Distinct from the dynamical phase, in a cyclic evolution, a system's state may acquire an additional component, a.k.a. geometric phase. The latter is a manifestation of a closed path in state space. Geometric phases underlie various…
Extended one- and two-dimensional defects in crystalline materials are usually metastable. The thermodynamic ground state of the material is presumed to be defect-free. Here, we investigate the conditions under which extended defects, such…
Designing the phase behavior of multicomponent mixtures is a rich area with many potential applications. One key question is how more than $M+1$ phases, as would normally be allowed by Gibbs' phase rule at generic temperature in a mixture…
We show that one can employ well-established numerical continuation methods to efficiently calculate the phase diagram for thermodynamic systems. In particular, this involves the determination of lines of phase coexistence related to first…