Information geometry, phase transitions, and the Widom line: Magnetic and liquid systems

Dey, Anshuman; Roy, Pratim; Sarkar, Tapobrata

doi:10.1016/j.physa.2013.09.017

Cited by 41 publications

(34 citation statements)

References 27 publications

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“…Moreover the R-crossing method has been tested in systems with different features: in [16,21] it has been applied to construct the vaporliquid coexistence line for the Lennard-Jones fluids, finding striking agreement with other methods; in [22] the authors studied the geometry of the thermodynamics of first and second order phase transitions of mean-field Curie-Weiss model (ferromagnetic systems) and also of liquidliquid phase transitions. Another field of application of the R-crossing method is the study of phase transitions of cosmological interest: in [23] the authors studied the liquid-gas like fist order phase transition in dyonic charged AdS black hole and in [24] the Hawking-Page transitions in Gauss-Bonnet-AdS black holes.…”

Section: A R-crossing Methodsmentioning

confidence: 99%

Thermodynamic geometry of strongly interacting matter

2018

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The thermodynamic geometry formalism is applied to strongly interacting matter to estimate the deconfinement temperature. The curved thermodynamic metric for Quantum Chromodynamics (QCD) is evaluated on the basis of lattice data, whereas the hadron resonance gas model is used for the hadronic sector. Since the deconfinement transition is a crossover, the geometric criterion used to define the (pseudo-)critical temperature, as a function of the baryonchemical potential µ B , is R(T, µ B ) = 0, where R is the scalar curvature. The (pseudo-)critical temperature, T c , resulting from QCD thermodynamic geometry is in good agreement with lattice and phenomenological freeze-out temperature estimates. The crossing temperature, T h , evaluated by the hadron resonance gas, which suffers of some model dependence, is larger than T c (about 20%) signaling remnants of confinement above the transition.PACS numbers:

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Section: A R-crossing Methodsmentioning

confidence: 99%

Thermodynamic geometry of strongly interacting matter

2018

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“…R, one can build up the transition curve by imposing the continuity of R. The RCM, coherent with Widom's microscopic description of the liquidgas coexistence region (i.e. with the idea that the correlation lengths of the two phases must be the same at the transition) has been tested in systems with different features: vapor-liquid coexistence line for the Lennard-Jones fluids [9,10], first and second order phase transitions of mean-field Curie-Weiss model (ferromagnetic systems), liquid-liquid phase transitions [11], phase transitions of cosmological interest as the liquid-gaslike first order phase transition in dyonic charged AdS black hole [12]. Another criterion, applied in the study of first order phase transitions in real fluids [18] and Lennard-Jones systems [10] is a first kind discontinuity in R.…”

Section: B Phase Transition In Thermodynamic Geometrymentioning

confidence: 99%

Thermodynamic geometry of Nambu–Jona Lasinio model

2020

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The formalism of Riemannian geometry is applied to study the phase transitions in Nambu -Jona Lasinio (NJL) model. Thermodynamic geometry reliably describes the phase diagram, both in the chiral limit and for finite quark masses. The comparison between the geometrical study of NJL model and of (2+1) Quantum Chromodynamics at high temperature and small baryon density shows a clear connection between chiral symmetry restoration/breaking and deconfinement/confinement regimes.

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“…A contribution of the geometry of thermodynamics is that it offers a thermodynamic link to the correlation length via the equality Eq. 20), and this is useful in calculating the Widom line [8,10,84,85,86].…”

Section: The Widom Linementioning

confidence: 99%

Thermodynamic metric geometry of the two-state ST2 model for supercooled water

Mausbach

May

Ruppeiner

2019

The Journal of Chemical Physics

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Liquid water has anomalous liquid properties, such as its density maximum at 4 • C. An attempt at theoretical explanation proposes a liquid-liquid phase transition line in the supercooled liquid state, with coexisting low-density (LDL) and high-density (HDL) liquid states. This line terminates at a critical point. It is assumed that the LDL state possesses mesoscopic tetrahedral structures that give it solidlike properties, while the HDL is a regular random liquid. But the short-lived nature of these solid-like structures make them difficult to detect directly. We take a thermodynamic approach instead, and calculate the thermodynamic Ricci curvature scalar R in the metastable liquid regime. It is believed that solid-like structures signal their presence thermodynamically by a positive sign for R, with a negative sign typically present in less organized fluid states. Using thermodynamic data from ST2 computer simulations fit to a mean field (MF) two state equation of state, we find significant regimes of positive R in the LDL state, supporting the proposal of solid-like structures in liquid water. In addition, we review the theory, compute critical exponents, demonstrate the large reach of the MF critical regime, and calculate the Widom line using R. point, two-state equation of state, ST2 models, solid-like liquid water, critical type fluctuation, Widom line, correlation length.

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Information geometry, phase transitions, and the Widom line: Magnetic and liquid systems

Cited by 41 publications

References 27 publications

Thermodynamic geometry of strongly interacting matter

Thermodynamic geometry of strongly interacting matter

Thermodynamic geometry of Nambu–Jona Lasinio model

Thermodynamic metric geometry of the two-state ST2 model for supercooled water

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