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 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.

A crystallographic study of the second-order phase transition in bis(p-toluene sulphonate) diacetylene polymer crystals

1980 ◽  
Vol 69 ◽  
pp. 49 ◽  
Author(s):  
Richard L. Williams ◽  
David Bloor ◽  
David N. Batchelder ◽  
Michael B. Hursthouse ◽  
William B. Daniels
Keyword(s):  
Phase Transition ◽  
Order Phase Transition ◽  
Second Order ◽  
Polymer Crystals ◽  
Crystallographic Study ◽  
Second Order Phase Transition

Second-order phase transition of high isotactic polypropylene at high temperature

Polymer ◽  
2002 ◽  
Vol 43 (4) ◽  
pp. 1473-1481 ◽  
Author(s):  
Fangming Gu ◽  
Masamichi Hikosaka ◽  
Akihiko Toda ◽  
Swapan Kumar Ghosh ◽  
Shinichi Yamazaki ◽  
...  
Keyword(s):  
Phase Transition ◽  
High Temperature ◽  
Isotactic Polypropylene ◽  
Order Phase Transition ◽  
Second Order ◽  
Second Order Phase Transition
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