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¨ *Research in Thermodynamics of
Space-times with Causal Boundaries *

**Entanglement, thermodynamics & area
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Interpreting the thermodynamic properties of black holes (BHs) and other space-times (STs) with horizons and uncovering their underlying statistical mechanics remains a challenge in spite of the intense efforts and the progress that has been achieved over the last 30 years. What does the black hole entropy measure, the degeneracy of microstates, entanglement entropy between the inside and outside of the horizon, or some intrinsic gravitational entropy? Is the quantum mechanics of STs with causal boundaries unitary? If so, why do some of them look thermal and non-unitary in some approximation?

Aiming to understand the physics of STs with causal boundaries, we pursue the entanglement point of view: that their statistical properties arise because classical observers access only a part of the whole quantum state and hence describe physics by the density matrix which results from tracing over the inaccessible degrees of freedom. The entanglement approach considers the fundamental physical objects describing the physics of STs with causal boundaries to be their global quantum state and the unitary evolution operator. An important consequence is that quantum correlations can exist across causal boundaries even if they are classically impossible, and, paradoxically, they can have observable consequences.

The entanglement explanation has several obvious advantages: it leads naturally to area-law entropy, it can incorporate the observer dependence of BH thermodynamics, and it can be applied to all forms of causal boundaries. However, entanglement entropy and entanglement correlation functions suffer from ultraviolet divergences near the horizon, which depend on the number of fields, unlike BH entropy which is finite and does not depend on the number of fields. In addition there are space-times for which it is unclear how to apply the entanglement approach.

We were able to show that due to entanglement, quantum fluctuations of non-relativistivistic systems, such as Bose-Einstein condensates, may differ significantly from standard statistical fluctuations and could, perhaps, be measured.