Thermodynamic geometry and deconfinement temperature

Abstract

The application of Riemannian geometry to the analysis of the equilibrium thermodynamics in Quantum Chromodynamics (QCD) at finite temperature and baryon density gives a new method to evaluate the critical temperature, T c , of the deconfinement transition. In the confined phase, described by the thermodynamic geometry of the Hadron Resonance Gas, the estimate of T c turns out completely consistent with lattice QCD simulations of the quark-gluon plasma phase if the hadron excluded volume and the interaction effects are taken into account.

Thermodynamic geometry of Nambu–Jona Lasinio model

“…More recently [14,15], TD has been applied to field theories and, in particular, to Quantum-Chromodynamics (QCD) at large temperature and low baryon density, to evaluate the (pseudo-) critical deconfinement temperature T c and to compare the results with the Hadron Resonance Gas models.…”

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].…”

“…On the other hand, for AdS BHs, R TG always points to attractive interaction. Although, in other systems, changes of sign of R TG have been seen [23][24][25] near the critical point (and, although recent general results, on the fundamental quantum gravitational interaction, indicate a fermionic nature of such degrees of freedom [72]), we take here the view that the physical region for Schwarzschild BHs in conformal gravity requires an entropy greater than the S 0 in Eq. (69), in order to have a consistent interpretation with the attractive nature of the gravitational interaction.…”

Thermodynamic geometry of the Gaussian core model fluid

“…There have been numerous applications of thermodynamic geometry to problems, including Ising based models [7,8,9,10,11,12], Bose and Fermi gases [13,14,15,16], and quantum chromodynamics [17]. In addition, the Riemannian geometry has become increasingly important in the field of fluid thermodynamics.…”