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We construct a novel approach, based on thermodynamic geometry, to characterize first-order phase transitions from a microscopic perspective, through the scalar curvature in the equilibrium thermodynamic state space. Our method resolves key theoretical issues in macroscopic thermodynamic constructs, and furthermore characterizes the Widom line through the maxima of the correlation length, which is captured by the thermodynamic scalar curvature. As an illustration of our method, we use it in conjunction with the mean field Van der Waals equation of state to predict the coexistence curve and the Widom line. Where closely applicable, it provides excellent agreement with experimental data. The universality of our method is indicated by direct calculations from the NIST database.
We present a study of phase transitions of the Curie--Weiss Potts model at (inverse) temperature $beta$, in presence of an external field $h$. Both thermodynamic and topological aspects of these transitions are considered. For the first aspect we com
We study information theoretic geometry in time dependent quantum mechanical systems. First, we discuss global properties of the parameter manifold for two level systems exemplified by i) Rabi oscillations and ii) quenching dynamics of the XY spin ch
Nonanalyticities of thermodynamic functions are studied by adopting an approach based on stationary points of the potential energy. For finite systems, each stationary point is found to cause a nonanalyticity in the microcanonical entropy, and the fu
When a second-order phase transition is crossed at fine rate, the evolution of the system stops being adiabatic as a result of the critical slowing down in the neighborhood of the critical point. In systems with a topologically nontrivial vacuum mani
We study the thermodynamic curvature, $R$, around the chiral phase transition at finite temperature and chemical potential, within the quark-meson model augmented with meson fluctuations. We study the effect of the fluctuations, pions and $sigma$-mes