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We generalize Ehrenfests 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 $frac{N(N+1)^{2}}{2}$ 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.
In this paper,we have studied phase transitions of higher dimensional charge black hole with spherical symmetry. we calculated the local energy and local temperature, and find that these state parameters satisfy the first law of thermodynamics. We an
In this paper, we extend the study of the relationship between the photon sphere and the thermodynamic phase transition, especially the reentrant phase transition, to this black hole background. According to the number of the thermodynamic critical p
The accretion of phantom fields by black holes within a thermodynamic context is addressed. For a fluid violating the dominant energy condition, case of a phantom fluid, the Euler and Gibbs relations permit two different possibilities for the entropy
The generalized Proca theories with second-order equations of motion can be healthily extended to a more general framework in which the number of propagating degrees of freedom remains unchanged. In the presence of a quartic-order nonminimal coupling
Searching for the effect of quintessence dark energy on the kinetics of black hole phase transition, we investigate in detail the dynamic phase transition of charged AdS black holes surrounded by quintessence in this paper. Based on the Gibbs free en