In this work we investigate the THERMAL ENTANGLEMENT between two-level atoms and photons in a nonlinear cavity. We consider intensity-dependent couplings and calculate the negativity, as a measure of atom-photon ENTANGLEMENT. The cavity is assumed to be at a temperature T, so that all number of photons, and at the same time, both atomic states, with definite probabilities, are present. We then demonstrate a condition under which the intensity-dependent coupling leads to ENTANGLEMENT. It is also shown that, as in the case of linear Jaynes- Cummings model, the THERMAL states of atoms and photons are never separable.

In 2006, Ryu and Takayanagi (RT) pointed out that (with a suitable cutoff) the ENTANGLEMENT entropy between two complementary regions of an equal-time surface of a d+1-dimensional conformal field theory on the conformal boundary of AdS{d+2} is, when the AdS radius is appropriately related to the parameters of the CFT, equal to 1/4G times the area of the $d$-dimensional minimal surface in the AdS bulk which has the junction of those complementary regions as its boundary, where $G$ is the bulk Newton constant. (More precisely, RT showed this for d=1 and adduced evidence that it also holds in many examples in d>1. ) We point out here that the RT-equality implies that, in the quantum theory on the bulk AdS background which is related to the boundary CFT according to Rehren's 1999 algebraic holography theorem, the ENTANGLEMENT entropy between two complementary bulk Rehren wedges is equal to one 1/4G times the (suitably cut off) area of their shared ridge. (This follows because of the geometrical fact that, for complementary ball-shaped regions, the RT minimal surface is precisely the shared ridge of the complementary bulk Rehren wedges which correspond, under Rehren's bulk-wedge to boundary double-cone bijection, to the complementary boundary double-cones whose bases are the RT complementary balls. ) This is consistent with the Bianchi-Meyers conjecture--that, in a theory of quantum gravity, the ENTANGLEMENT entropy, S between the degrees of freedom of a given region with those of its complement takes the form S = A/4G (plus lower order terms)--but only if the phrase `degrees of freedom' is replaced by `matter degrees of freedom'. It also supports related previous arguments of the author--consistent with the author's `matter-gravity ENTANGLEMENT hypothesis'--that the AdS/CFT correspondence is actually only a bijection between just the matter (i. e. non-gravity) sector operators of the bulk and the boundary CFT operators.

In this work, we explore the holographic ENTANGLEMENT entropy with an infinite strip region of the boundary in Horndeski gravity. In our prescription we consider the spherically and planar topologies black holes in the AdS4/CFT3 scenario. In such framework, we show the behavior of the ENTANGLEMENT entropy in function of the Horndeski parameters. Such parameters modify the information store of subsystem A, especially when the parameter $gamma$ increases the information about the subsystem will also increase or decrease when it decreases. Thus, with this scheme we compute the “first law of ENTANGLEMENT thermodynamics” in Horndeski gravity and we show that a very small subsystem obeys the analogous property of the first law of thermodynamics if we excite the system.

In this work‎, ‎we explore the ENTANGLEMENT entropy equipped with the $\kappa$-algebra‎. ‎This ENTANGLEMENT entropy is computed through the geometric setup as performed by Hartman-Maldacena‎, ‎which‎, ‎in their prescription‎, ‎finds that the entropy grows linearly in time‎. ‎In our case‎, ‎we show that the $\kappa$-algebra embedding provides a richer scenario where the third-order corrections in time added from $\kappa$-algebra to ENTANGLEMENT entropy imply that the growth of quantum correlations between subsystems is more intricate than a simple linear increase into the dynamics of black hole THERMALization and quantum information flow‎. ‎In the context of holography‎, ‎such corrections suggest that the THERMALization process is not instantaneous but involves higher-order interactions between subsystems‎.