Relative entropy and the Bekenstein bound

By H. Casini. 2008

301 citations recorded by the source corpus.

Elaborating on a previous work by Marolf et al, we relate some exact results in quantum field theory and statistical mechanics to the Bekenstein universal bound on entropy. Specifically, we consider the relative entropy between the vacuum and another state, both reduced to a local region. We propose that, with the adequate interpretation, the positivity of the relative entropy in this case constitutes a well-defined statement of the bound in flat space. We show that this version arises naturally from the original derivation of the bound from the generalized second law when quantum effects are taken into account. In this formulation the bound holds automatically, and in particular it does not suffer from the proliferation of the species problem. The results suggest that while the bound is relevant at the classical level, it does not introduce new physical constraints semiclassically.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/bfb7f7bc41ce4be608e34a60a6deda1f7a1a0e8a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. R. Myers
2. D. Harlow
3. T. Faulkner
4. Aitor Lewkowycz
5. E. Witten
6. T. Nishioka
7. J. Maldacena
8. S. Raju

In Nuclear and High Energy Physics

1. R. Myers
2. D. Harlow
3. T. Faulkner
4. T. Takayanagi
5. J. Maldacena
6. D. Stanford
7. S. Raju
8. Aitor Lewkowycz

In Statistical and Nonlinear Physics

1. R. Myers
2. D. Harlow
3. T. Faulkner
4. J. Maldacena
5. L. Susskind
6. D. Stanford
7. S. Raju
8. E. Witten

Citations in the corpus

• Modular Hamiltonians on the null plane and the Markov property of the vacuum state (2017, background): “Among applications of the relative entropy to QFT we can mention the proof of the Bekenstein bound [10, 11], the quantum averaged null energy condition (ANEC) [12, 13], and results on the monotonicity of renormalization group (RG) flows [14, 15].”
• A proof of the generalized second law for rapidly changing fields and arbitrary horizon slices (2011, methodology): “The relationship between the relative and generalized entropies was made explicit in Casini [32], and was used in my earlier proof of the GSL for Rindler wedges [12].”
• Proof of the Quantum Null Energy Condition (2015, background): “(The QFC is distinct from the quantum Bousso bound of [39, 40], which defines the entropy by vacuum subtraction [41], a procedure applicable if the gravitational effects of matter are negligible.”
• Holographic Complexity Equals Bulk Action? (2015, background): “Black holes are known to excel at information theoretic tasks: they are the densest memory [11–15]; they are the fastest scramblers [16–18].”
• Emergent Gravity and the Dark Universe (2016, background): “which up to a sign is the familiar Bekenstein bound [56], which together with the results of [57] suggests that the definition of mass in emergent gravity is given in terms of relative entropy.”
• Gravity and the crossed product (2021, background): “Another analogy is with the many problems, such as those studied in [23, 24], in which entanglement entropy differences in quantum field theory are better defined than entanglement entropies.”
• The Swampland: Introduction and Review (2019, background): “However, it was shown in [43], building on earlier ideas in [44,45], that the bound is not violated even in the limit Ns →∞.”
• Jerusalem Lectures on Black Holes and Quantum Information (2014, background): “Recently however Casini has given a simple and elegant proof that a precise version of the bound holds in any relativistic quantum field theory [78].”
• APS Medal for Exceptional Achievement in Research: Invited article on entanglement properties of quantum field theory (2018, methodology): “Positivity of relative entropy has various applications in quantum field theory, for instance in the interpretation and proof (Casini, 2008; Longo and Xu, 2018) of the Bekenstein bound on the energy, entropy, and size of a quantum system.”
• Notes on Some Entanglement Properties of Quantum Field Theory (2018, background): “Positivity of relative entropy has various applications in quantum field theory, for instance in the interpretation and proof [50,51] of the Bekenstein bound on the energy, entropy, and size of a quantum system.”
• Relative entropy equals bulk relative entropy (2015, background): “It has also played an important role in formulating a precise version of the Bekenstein bound [3] and arguments for the second law of black hole thermodynamics [4, 5].”
• Modular Hamiltonians for deformed half-spaces and the averaged null energy condition (2016, unknown): “Similarly, the properties of relative entropy have been used to prove several interesting results such as the Bekenstein bound [15], the generalized second law for causal horizons [16] and the covariant entropy bound in the context of semi-classical gravity [3, 4].”
• A general proof of the quantum null energy condition (2017, background): “It would also be interesting to study this in free theories extending the proof of the QNEC for free QFTs [24].23”