scholarly journals Generalized Ehrenfest's equations and phase transition in black holes

2015 ◽  
Vol 24 (03) ◽  
pp. 1550029 ◽  
Author(s):  
Mohammad Bagher Jahani Poshteh ◽  
Behrouz Mirza ◽  
Fatemeh Oboudiat
Keyword(s):  
Phase Transition ◽  
Black Holes ◽  
Critical Point ◽  
Order Phase Transition ◽  
Arbitrary Number ◽  
Degrees Of Freedom ◽  
Second Order ◽  
First Law Of Thermodynamics ◽  
Three Degrees Of Freedom ◽  
Second Order Phase Transition

In this paper, we generalize Ehrenfest's equations to systems having two work terms, i.e. systems with three degrees of freedom. For black holes with two work terms we obtain nine equations instead of two to be satisfied at the critical point of a second-order phase transition. We finally generalize this method to a system with an arbitrary number of degrees of freedom and found there is [Formula: see text] equations to be satisfied at the point of a second-order phase transition where N is number of work terms in the first law of thermodynamics.

The universal Ehrenfest scheme on black holes

2015 ◽  
Vol 30 (36) ◽  
pp. 1550187 ◽  
Author(s):  
Li-Chun Zhang ◽  
Ren Zhao
Keyword(s):  
Phase Transition ◽  
Black Holes ◽  
Thermodynamic Functions ◽  
Order Phase Transition ◽  
Thermodynamic System ◽  
Second Order ◽  
First Law Of Thermodynamics ◽  
Jacobi Determinant ◽  
Second Order Phase Transition

By use of the Jacobi determinant, we verify that, for a thermodynamic system which satisfies the first law of thermodynamics, if only there is second-order phase transition in the system, the Prigogine–Defay ratio is the constant 1. This conclusion is universal and independent of the concrete forms of the thermodynamic functions and also apply to black holes.

scholarly journals Big Bang as a Critical Point

2017 ◽  
Vol 2017 ◽  
pp. 1-5 ◽  
Author(s):  
Jakub Mielczarek
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Quantum Gravity ◽  
Critical Point ◽  
Order Phase Transition ◽  
Big Bang ◽  
Second Order ◽  
Extended Phase ◽  
Causal Dynamical Triangulations ◽  
Second Order Phase Transition

This article addresses the issue of possible gravitational phase transitions in the early universe. We suggest that a second-order phase transition observed in the Causal Dynamical Triangulations approach to quantum gravity may have a cosmological relevance. The phase transition interpolates between a nongeometric crumpled phase of gravity and an extended phase with classical properties. Transition of this kind has been postulated earlier in the context of geometrogenesis in the Quantum Graphity approach to quantum gravity. We show that critical behavior may also be associated with a signature change in Loop Quantum Cosmology, which occurs as a result of quantum deformation of the hypersurface deformation algebra. In the considered cases, classical space-time originates at the critical point associated with a second-order phase transition. Relation between the gravitational phase transitions and the corresponding change of symmetry is underlined.

Second Order Phase Transition in a Highly Chaotic Hamiltonian System with Many Degrees of Freedom

1997 ◽  
Vol 07 (04) ◽  
pp. 839-847 ◽  
Author(s):  
Yoshiyuki Y. Yamaguchi
Keyword(s):  
Phase Transition ◽  
Hamiltonian System ◽  
Order Phase Transition ◽  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Phenomenological Theory ◽  
Critical Energy ◽  
Second Order ◽  
Slow Relaxations ◽  
Second Order Phase Transition

Second order phase transition is numerically investigated in a Hamiltonian system with many degrees of freedom. Slow relaxations of power type are observed for some initial conditions at critical energy of phase transition. This is consisent with a result of a phenomenological theory of statistical mechanics. On the other hand, the slow relaxations show that the system stays in non-equilibrium states for a while, and that phenomenon does not agree with a result of the theory. To understand the slow relaxation, theories for perturbed systems cannot be applied since near the critical energy the system is highly chaotic rather than nearly integrable. The thresholds of the highly chaotic systems is different from the critical energy of phase transition.

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