From the black hole thermodynamics point of view, we show that the entropy function $\mathbf{f}$ and the free energy $F$ are related via $\mathbf{f}=e_{I}q_{I}+Ω_Hq_I{A_ϕ^I}'-\frac{\partial F}{\partial r} |_{r_{H}}$. Assuming the entropy function is known for extremal black holes, we propose an approach to calculate the entropy of non-extremal cases by slightly moving the extremal black hole geometry from extremality. The entropy of non-extremal $D1D5$- and $D1D5p$-branes in the presence of higher derivative corrections are computed as concrete examples. An attempt has also been made to explain why the entropy function method can calculate the corrected entropy without knowing the exact form of black hole solution in higher derivative gravity theories.
It has been shown that the entropy function formalism is an efficient way to calculate the entropy of black holes in string theory. We check this formalism for the extremal charged dilaton black hole. We find the general four-derivative correction on the black hole entropy from the value of the entropy function at its extremum point.
From black hole thermodynamics, the Bekenstein bound has been proposed as a universal thermal entropy bound. It has been further generalized to an entanglement entropy bound which is valid even in a quantum system. In a quantumly entangled system, the non-negativity of the relative entropy leads to the entanglement entropy bound. When the entanglement entropy bound is saturated, a quantum system satisfies the thermodynamics-like law with an appropriately defined entanglement temperature. We show that the saturation of the entanglement entropy bound accounts for a universal feature of the entan…
We consider charged black holes in four dimensional AdS space, in the presence of a Weyl correction. We obtain the solution including the effect of back-reaction, perturbatively up to first order in the Weyl coupling, and study its thermodynamic properties. This is complemented by a calculation of the holographic entanglement entropy of the boundary theory. The consistency of results obtained from both computations is established.
Thermodynamics is usually developed starting from entropy and the maximum entropy principle. We investigate here to what extent one can replace entropy with relative entropy which has several advantages, for example in the context of local quantum field theory. We find that the principle of maximum entropy can be replaced by a principle of minimum expected relative entropy. Various ensembles and their thermodynamic potentials can be defined through relative entropy. We also show that thermal fluctuations are in fact governed by a relative entropy. Furthermore we reformulate the third law of th…
We explore the thermodynamic analysis at the apparent horizon in the framework of Rastall theory of gravity. We take different entropies such as the Bakenstein, logarithmic corrected, power law corrected, and the Renyi entropies. We investigate the first law and generalized second law of thermodynamics analytically for these entropies which hold under certain conditions. Furthermore, the behavior of the total entropy in each case is analyzed. As a result, it is implied that the generalized second law of thermodynamics is satisfied. We also check whether the thermodynamic equilibrium condition …
The extended black hole thermodynamics in which the cosmological constant plays the role of pressure significantly enriches the phase structure of the theory. In order to understand the extended black hole thermodynamics more precisely, we let the value of the cosmological constant vary dynamically via tunneling from one vacuum to another in a black hole induced vacuum decay. In this process, entropy of the matter/energy released by a black hole is crucial to validate the second law of thermodynamics. In other words, without taking this bulk entropy into account, entropy associated with the bl…
We discuss the first law of thermodynamics of Bardeen black hole. The presence of magnetic monopole charge modifies the energy and we define the temperature of the system accordingly. We introduce a lower cut-off to the space time by introducing a spherical surface, which can be identified with the event horizon. The corresponding temperature is identified with Hawking temperature. The entropy is assumed to obey the area law and we confirm this by calculating the statistical entropy by using brick wall model.
We investigate the validity of the generalized second law of thermodynamics, applying Barrow entropy for the horizon entropy. The former arises from the fact that the black-hole surface may be deformed due to quantum-gravitational effects, quantified by a new exponent $Δ$. We calculate the entropy time-variation in a universe filled with the matter and dark energy fluids, as well as the corresponding quantity for the apparent horizon. We show that although in the case $Δ=0$, which corresponds to usual entropy, the sum of the entropy enclosed by the apparent horizon plus the entropy of the hori…
A dispersive medium becomes entangled with zero-point fluctuations in the vacuum. We consider an arbitrary array of material bodies weakly interacting with a quantum field and compute the quantum mutual information between them. It is shown that the mutual information in D dimensions can be mapped to classical thermodynamic entropy in D+1 dimensions. As a specific example, we compute the mutual information both analytically and numerically for a range of separation distances between two bodies in D=2 dimensions and find a logarithmic correction to the area law at short separations. A key advan…
