All entropy is entanglement entropy. This appears as the result of the existence of black holes. The origin of entropy and the way in which it defines the perceived time direction in macroscopic systems has been discussed and can be debated as long as one ignores black holes. In such a case, thermodynamic entropy may define the arrow of time and entanglement entropy defines some special globally defined entropy encoding information in a non-local sense. With black holes however, if we accept that in-falling objects must have their information encoded outside, for example through non-local fluctuations away from thermalisation of the Hawking radiation, and that the horizon of a black hole cuts all classical information from the outside, then all the entropy that can be added to the black hole, which is basically any form of entropy, must be translated into some form of entanglement entropy to be detected outside. A discussion about the nature of information channels shows that spacetime may not be a correlation-insensitive channel as usually employed in the engineering of quantum computing. Time may emerge as a property of the complexity of entanglement spreading.
All entropy is entanglement entropy. This appears as the result of the existence of black holes. The origin of entropy and the way in which it defines the perceived time direction in macroscopic systems has been discussed and can be debated as long as one ignores black holes. In such a case, thermodynamic entropy may define the arrow of time and entanglement entropy defines some special globally defined entropy encoding information in a non-local sense. With black holes however, if we accept that in-falling objects must have their information encoded outside, for example through non-local fluctuations away from thermalisation of the Hawking radiation, and that the horizon of a black hole cuts all classical information from the outside, then all the entropy that can be added to the black hole, which is basically any form of entropy, must be translated into some form of entanglement entropy to be detected outside. A discussion about the nature of information channels shows that spacetime may not be a correlation-insensitive channel as usually employed in the engineering of quantum computing. Time may emerge as a property of the complexity of entanglement spreading.
The thermodynamic entropy of an isolated system is given by its von Neumann entropy. Over the last few years, there has been an intense activity to understand the thermodynamic entropy from the principles of quantum mechanics. More specifically, is there a relation between the (von Neumann) entropy of entanglement between a system and some (separate) environment and the thermodynamic entropy? It is difficult to obtain the relation for many body systems, hence, most of the work in the literature has focused on small number systems. In this work, we consider black holes—which are simple yet macroscopic systems—and show that a direct connection could not be made between the entropy of entanglement and the Hawking temperature. In this work, within the adiabatic approximation, we explicitly show that the Hawking temperature is indeed given by the rate of change of the entropy of entanglement across a black hole’s horizon with regard to the system energy. This is yet other numerical evidence leading to understanding the key features of black-hole thermodynamics from the viewpoint of quantum information theory.
This work explores the hypothesis that time is an emergent phenomenon arising from underlying quantum informational processes. By integrating principles from quantum mechanics, thermodynamics, and general relativity, we develop a comprehensive framework that elucidates the relationship between quantum complexity, entanglement, and the nature of time. We investigate the role of quantum complexity in the evolution of quantum states and demonstrate how the increase in entanglement entropy provides a microscopic basis for the arrow of time. Using the AdS/CFT correspondence and the holographic principle, we establish connections between spacetime geometry and quantum informational measures like entanglement entropy. We address the black hole information paradox within this context, arguing that information is preserved in a highly scrambled form. Additionally, we propose an experimental design using black hole analogues to empirically validate our theoretical predictions, focusing on fast scrambling and the growth of quantum complexity. Our findings suggest that quantum informational dynamics govern the emergence of time and spacetime geometry. This work bridges quantum mechanics, thermodynamics, information theory, and general relativity, offering potential applications in quantum technologies and new insights into the fundamental nature of reality.
The black hole information puzzle arises from a discrepancy between conclusions drawn from general relativity and quantum theory about the nature of the radiation emitted by a black hole. According to Hawking's original argument, the radiation is thermal and its entropy thus increases monotonically as the black hole evaporates. Conversely, due to the reversibility of time evolution according to quantum theory, the radiation entropy should start to decrease after a certain time, as predicted by the Page curve. This decrease has been confirmed by new calculations based on the replica trick, which also exhibit its geometrical origin: spacetime wormholes that form between the replicas. Here we analyse the discrepancy between these and Hawking's original conclusions from a quantum information theory viewpoint, using in particular the quantum de Finetti theorem. The theorem implies the existence of extra information, W, which is neither part of the black hole nor the radiation, but plays the role of a reference. The entropy obtained via the replica trick can then be identified to be the entropy S(R∣W) of the radiation conditioned on the reference W, whereas Hawking's original result corresponds to the non-conditional entropy S(R). The entropy S(R∣W), which mathematically is an ensemble average, gains an operational meaning in an experiment with N independently prepared black holes: For large N, it equals the normalised entropy of their joint radiation, S(R1⋯RN)/N. The discrepancy between this entropy and S(R) implies that the black holes are correlated. The replica wormholes may thus be interpreted as the geometrical representation of this correlation. Our results also suggest a many-black-hole extension of the widely used random unitary model, which we support with non-trivial checks.
Entanglement entropy is often speculated as a strong candidate for the origin of black-hole entropy. To judge whether or not this speculation is true, it is effective to investigate the whole structure of thermodynamics obtained from the entanglement entropy, rather than just to examine the apparent structure of the entropy alone or to compare it with that of black-hole entropy. This is because entropy acquires a physical significance only when it is related to the energy and the temperature of a system. From this point of view, we construct a ``thermodynamics of entanglement'' by introducing an entanglement energy and compare it with black-hole thermodynamics. We consider two possible definitions of entanglement energy. Then we construct two different kinds of thermodynamics by combining each of these different definitions of entanglement energy with the entanglement entropy. We find that both of these two kinds of thermodynamics show significant differences from black-hole thermodynamics if no gravitational effects are taken into account. These differences are, in particular, highlighted in the context of the third law of thermodynamics. Finally we see how the inclusion of gravity alters the thermodynamics of the entanglement. We give a suggestive argument that the thermodynamics of the entanglement behaves like black-hole thermodynamics if the gravitational effects are included properly. Thus the entanglement entropy passes a nontrivial check to be the origin of black-hole entropy.
The black-hole information paradox is usually formulated as a conflict between two semiclassical statements: Hawking evaporation appears to radiate away mass in a nearly thermal manner, while unitary quantum dynamics forbids the destruction of information. In this paper we construct a macroscopic black-hole surrogate inside the discrete, background-free Quantum Graph Emergent Field Theory (QGEFT) and track both horizon-entanglement proxies and the topological fate of explicitly injected information. Starting from a thermalized Unified Phase 3 universe with N = 1024 sites, we force a localized geometric collapse by driving one node to target degree k = 160, then inject a structured quark-like defect whose internal edges are tracked exactly through 100 subsequent Monte Carlo sweeps. The key observable is a horizon cut-size proxy: the number of edges crossing between the black-hole region and the exterior vacuum, together with a normalized entanglement proxy built from that cut. In the present benchmark the horizon cut-size rises from 1027 to a peak of 1030 edges at sweep 1, while the normalized cut-based entanglement proxy rises from 2.7483 to 2.7563, then trends downward with fluctuations to 2.5941 by sweep 100 as the black-hole core shrinks from degree 161 to 132. At the same time, direct tracking of the infalling quark reveals incomplete local reconstruction: only 25% of the tracked edges appear outside the horizon as distinct edges at any given sampled frame, and the best structural-overlap score reaches only 0.3946. The narrow conclusion supported by the current data is therefore mixed. The black hole exhibits a real topological evaporation channel and a measurable Page-like turnover in the horizon entanglement proxy, but local observables remain Hawking-leaning and do not by themselves recover the full infalling structure. In the QGEFT interpretation, this is evidence for fast scrambling rather than literal information destruction: the information is not recovered as a small intact motif, but is dispersed into the global topological microstate of the graph.
We consider black-hole evaporation from a hidden-variables perspective. It is suggested that Hawking information loss, associated with the transition from a pure to a mixed quantum state, is compensated for by the creation of deviations from Born-rule probabilities outside the event horizon. The resulting states have non-standard or 'nonequilibrium' distributions of hidden variables, with a specific observable signature - a breakdown of the sinusoidal modulation of quantum probabilities for two-state systems. Outgoing Hawking radiation is predicted to contain statistical anomalies outside the domain of the quantum formalism. Further, it is argued that even for a macroscopic black hole, if one half of an entangled EPR-pair should fall behind the event horizon, the other half will develop similar statistical anomalies. We propose a simple rule, whereby the relative entropy of the nonequilibrum (hidden-variable) distribution generated outside the horizon balances the increase in von Neumann entropy associated with the pure-to-mixed transition. It is argued that there are relationships between hidden-variable and von Neumann entropies even in non-gravitational physics. We consider the possibility of observing anomalous polarisation probabilities, in the radiation from primordial black holes, and in the atomic cascade emission of entangled photon pairs from black-hole accretion discs.