Thermodynamic geometry of the quark-meson model

Abstract

We study the thermodynamic geometry of the Quark-Meson model, focusing on the curvature, R, around the chiral crossover at finite temperature and baryon chemical potential. We find a peculiar behavior of R in the crossover region, in which the sign changes and a local maximum develops; in particular, the height of the peak of R in the crossover region becomes large in proximity of the critical endpoint and diverges at the critical endpoint. The appearance of a pronounced peak of R close to the critical endpoint supports the idea that R grows with the correlation volume around the phase transition. We also analyze the mixed fluctuations of energy and baryon number, ∆U ∆N , which grow up substantially in proximity of the critical endpoint: in the language of thermodynamic geometry these fluctuations are responsible for the vanishing of the determinant of the metric, which results in thermodynamic instability and are thus related to the appearance of the second order phase transition at the critical endpoint.

Stability of Schwarzschild (Anti)de Sitter black holes in conformal gravity

“…This way, critical phenomena are related to distinctive signs of the scalar curvature, R TG , obtained from such metric: R TG = 0 means a system made of noninteracting components, while for R TG < 0 such components attract each other, and for R TG > 0 repel each other. Moreover, R TG diverges in a second order phase transition as the correlation volume, while it appears to have a local maximum at a crossover, as happens in quantum chromodynamics [23][24][25][26][27]. TG has been tested in many different systems: phase coexistence for helium, hydrogen, neon and argon [28], for the Lennard Jones fluids [29,30], for ferromagnetic systems and liquid liquid phase transitions [31]; in the liquid gas like first order phase transition in dyonic charged AdS BH [32]; in quantum chromodynamics (QCD) to describe crossover from Hadron gas and Quark Gluon Plasma [23][24][25][26][27]; in the Hawking Page transitions in Gauss Bonnet AdS [33], Reissner Nordstrom AdS and the Kerr AdS [34].…”

“…Moreover, R TG diverges in a second order phase transition as the correlation volume, while it appears to have a local maximum at a crossover, as happens in quantum chromodynamics [23][24][25][26][27]. TG has been tested in many different systems: phase coexistence for helium, hydrogen, neon and argon [28], for the Lennard Jones fluids [29,30], for ferromagnetic systems and liquid liquid phase transitions [31]; in the liquid gas like first order phase transition in dyonic charged AdS BH [32]; in quantum chromodynamics (QCD) to describe crossover from Hadron gas and Quark Gluon Plasma [23][24][25][26][27]; in the Hawking Page transitions in Gauss Bonnet AdS [33], Reissner Nordstrom AdS and the Kerr AdS [34]. A list of results have been obtained by applying TG to BHs [35][36][37][38][39][40][41][42][43][44][45].…”

Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics

“…This is usually justified under the idea that the internal energy of the system, U is much bigger than the differences in energy of the quantum eigenstates, max ij | i − j | U . In order to better understand the continuous approximation (20) we will provide a first basic example. For the model of a particle in a three dimensional cubic box of edge length L, the quantum state will be defined by a triplet of integers, i = (n x , n y , n z ) and the energy state will be given by…”

“…Moreover, the meaning of the sign of the scalar curvature is also unclear. To the best of our knowledge, nowadays there is no common agreement on the this sign means [20].…”

“…In [21], Janyszek and Mrugala used the concept of quantum mechanical exchange effect to suggest a physical interpretation of the sign of the scalar curvature for ideal quantum gases. In the sign convention according to which the scalar curvature of a two-sphere of radius a is positive (that is, R = 2/a 2 ), it happens that [20][21][22][23]: i) R = 0 for an ideal classical gas; ii) R < 0 for an ideal FD gas; iii) R > 0 for an ideal BE gas. Janyszek and Mrugala [21] proposed to interpret the scalar curvature as an indicator of stability of the physical system under investigation, with the understanding that a stable system exhibits thermodynamically negligible fluctuations.…”