Information geometry and phase transitions
TLDR
In this paper, the information geometry for a number of solvable statistical-mechanical models has been studied and the scalar curvature of a non-interacting model has a flat geometry (R = 0) while R diverges at the critical point of an interacting one.Abstract:
The introduction of a metric onto the space of parameters in models in statistical mechanics and beyond gives an alternative perspective on their phase structure. In such a geometrisation, the scalar curvature, R , plays a central role. A non-interacting model has a flat geometry ( R =0) , while R diverges at the critical point of an interacting one. Here, the information geometry is studied for a number of solvable statistical–mechanical models.read more
Citations
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Geometrothermodynamics of black holes
TL;DR: In this article, the authors reformulated the thermodynamics of black holes in the context of geometrothermodynamics and showed that they are invariant with respect to Legendre transformations.
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Relating Fisher information to order parameters.
TL;DR: The framework presented here reveals the basic thermodynamic reasons behind similar empirical observations reported previously and highlights the generality of Fisher information as a measure that can be applied to a broad range of systems, particularly those where the determination of order parameters is cumbersome.
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P–V criticality and geometrical thermodynamics of black holes with Born–Infeld type nonlinear electrodynamics
TL;DR: In this paper, the authors take into account the black-hole solutions of Einstein gravity in the presence of logarithmic and exponential forms of nonlinear electrodynamics and study the critical behavior of the system in the context of heat capacity.
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$P-V$ criticality and geometrothermodynamics of black holes with Born-Infeld type nonlinear electrodynamics
TL;DR: In this paper, the authors consider the nonlinearity effects of nonlinear electrodynamics and see how the power of non-linearity affects critical behavior, and investigate the effects of dimensionality on critical values and analyze its crucial role.
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Thermodynamic Geometry Of Charged Rotating BTZ Black Holes
TL;DR: In this paper, the authors study the thermodynamics and the thermodynamic geometries of charged rotating Banados-Teitelboim-Zanelli black holes in (2+1)-gravity.
References
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On the Mathematical Foundations of Theoretical Statistics
TL;DR: In this paper, the authors define the center of location as the abscissa of a frequency curve for which the sampling errors of optimum location are uncorrelated with those of optimum scaling.
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Riemannian geometry and the thermodynamics of model magnetic systems
H. Janyszek,R. Mrugala +1 more
TL;DR: Introduction and etude d'une structure riemanienne de l'espace des parametres, pour des systemes magnetiques decrits dans le cadre de la statistique quantique, basee sur the conception of l'information relative.
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Information geometry of the spherical model.
TL;DR: The scaling behavior of the curvature R of the information geometry metric for the spherical model is calculated and it is found that R approximately epsilon(-2), where ePSilon=beta(c)-beta is the distance from criticality.
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On the Riemannian metrical structure in the classical statistical equilibrium thermodynamics
TL;DR: In this paper, the generalized Gibbs statistical states generated by a set of classical observables are considered and a concave hypersurface embedded in a linear space is shown to be a differential manifold with map given by statistical temperatures.
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Information geometry of the ising model on planar random graphs.
TL;DR: The solution in field of the Ising model is used on an ensemble of planar random graphs to evaluate the scaling behavior of the scalar curvature, and a plausible scaling relation is postulated: R approximately |beta-beta(c)|(alpha-2).