Mutual information challenges entropy bounds

We consider some formulations of the entropy bounds at the semiclassical level. The entropy S(V) localized in a region V is divergent in quantum field theory (QFT). Instead of it we focus on the mutual information I(V,W)=S(V)+S(W)-S(V\cup W) between two different non-intersecting sets V and W. This is a low energy quantity, independent of the regularization scheme. In addition, the mutual information is bounded above by twice the entropy corresponding to the sets involved. Calculations of I(V,W) in QFT show that the entropy in empty space cannot be renormalized to zero, and must be actually very large. We find that this entropy due to the vacuum fluctuations violates the FMW bound in Minkowski space. The mutual information also gives a precise, cutoff independent meaning to the statement that the number of degrees of freedom increases with the volume in QFT. If the holographic bound holds, this points to the essential non locality of the physical cutoff. Violations of the Bousso bound would require conformal theories and large distances. We speculate that the presence of a small cosmological constant might prevent such a violation.Comment: 10 pages, 2 figures, minor change

Remarks on the entanglement entropy for disconnected regions

Few facts are known about the entanglement entropy for disconnected regions in quantum field theory. We study here the property of extensivity of the mutual information, which holds for free massless fermions in two dimensions. We uncover the structure of the entropy function in the extensive case, and find an interesting connection with the renormalization group irreversibility. The solution is a function on space-time regions which complies with all the known requirements a relativistic entropy function has to satisfy. We show that the holographic ansatz of Ryu and Takayanagi, the free scalar and Dirac fields in dimensions greater than two, and the massive free fields in two dimensions all fail to be exactly extensive, disproving recent conjectures.Comment: 14 pages, 4 figures, some addition

Positivity, entanglement entropy, and minimal surfaces

The path integral representation for the Renyi entanglement entropies of integer index n implies these information measures define operator correlation functions in QFT. We analyze whether the limit $n\rightarrow 1$, corresponding to the entanglement entropy, can also be represented in terms of a path integral with insertions on the region's boundary, at first order in $n-1$. This conjecture has been used in the literature in several occasions, and specially in an attempt to prove the Ryu-Takayanagi holographic entanglement entropy formula. We show it leads to conditional positivity of the entropy correlation matrices, which is equivalent to an infinite series of polynomial inequalities for the entropies in QFT or the areas of minimal surfaces representing the entanglement entropy in the AdS-CFT context. We check these inequalities in several examples. No counterexample is found in the few known exact results for the entanglement entropy in QFT. The inequalities are also remarkable satisfied for several classes of minimal surfaces but we find counterexamples corresponding to more complicated geometries. We develop some analytic tools to test the inequalities, and as a byproduct, we show that positivity for the correlation functions is a local property when supplemented with analyticity. We also review general aspects of positivity for large N theories and Wilson loops in AdS-CFT.Comment: 36 pages, 10 figures. Changes in presentation and discussion of Wilson loops. Conclusions regarding entanglement entropy unchange

Hyperspherical entanglement entropy

The coefficient of the log term in the entanglement entropy associated with hyperspherical surfaces in flat space-time is shown to equal the conformal anomaly by conformally transforming Euclideanised space--time to a sphere and using already existing formulae for the relevant heat--kernel coefficients after cyclic factoring. The analytical reason for the result is that the conformal anomaly on the lune has an extremum at the ordinary sphere limit. A proof is given. Agreement with a recent evaluation of the coefficient is found.Comment: 7 pages. Final revision. Historical comments amended. Minor remarks adde

AdS/CFT and Strong Subadditivity of Entanglement Entropy

Recently, a holographic computation of the entanglement entropy in conformal field theories has been proposed via the AdS/CFT correspondence. One of the most important properties of the entanglement entropy is known as the strong subadditivity. This requires that the entanglement entropy should be a concave function with respect to geometric parameters. It is a non-trivial check on the proposal to see if this property is indeed satisfied by the entropy computed holographically. In this paper we examine several examples which are defined by annuli or cusps, and confirm the strong subadditivity via direct calculations. Furthermore, we conjecture that Wilson loop correlators in strongly coupled gauge theories satisfy the same relation. We also discuss the relation between the holographic entanglement entropy and the Bousso bound.Comment: 29 pages, harvmac, 7 figures, references adde

Localization of α-synuclein in teleost central nervous system: immunohistochemical and Western blot evidence by 3D5 monoclonal antibody in the common carp, Cyprinus carpio

Alpha synuclein (α-syn) is a 140 amino acid vertebrate-specific protein, highly expressed in the human nervous system and abnormally accumulated in Parkinson's disease and other neurodegenerative disorders, known as synucleinopathies. The common occurrence of α-syn aggregates suggested a role for α-syn in these disorders, although its biological activity remains poorly understood. Given the high degree of sequence similarity between vertebrate α-syns, we investigated this proteins in the CNS of the common carp Cyprinus carpio, with the aim of comparing its anatomical and cellular distribution with that of mammalian α-syn. The distribution of α-syn was analyzed by semiquantitative Western blot, immunohistochemistry and immunofluorescence by a novel monoclonal antibody (3D5) against a fully conserved epitope between carp and human α-syn. The distribution of 3D5 immunoreactivity was also compared with that of ChAT, TH and 5HT by double immunolabelings. Results show that α-syn-like protein of about 17 kDa is expressed to different levels in several brain regions and in the spinal cord. Immunoreactive materials were localized in neuronal perikarya and varicose fibers but not in the nucleus. Present findings indicate that α-syn-like proteins may be expressed in few subpopulations of catecholaminergic and serotoninergic neurons in the carp brain. However, evidence of cellular colocalization 3D5/TH or 3D5/5HT was rare. Differently, the same proteins appear to be co-expressed with ChAT by cholinergic neurons in several motor and reticular nuclei. These results sustain the functional conservation of the α-syn expression in cholinergic systems and suggest that α-syn modulates similar molecular pathways in phylogenetically distant vertebrates. This article is protected by copyright. All rights reserved

Numerical determination of entanglement entropy for a sphere

We apply Srednicki's regularization to extract the logarithmic term in the entanglement entropy produced by tracing out a real, massless, scalar field inside a three dimensional sphere in 3+1 flat spacetime. We find numerically that the coefficient of the logarithm is -1/90 to 0.2 percent accuracy, in agreement with an existing analytical result

Topological phases and topological entropy of two-dimensional systems with finite correlation length

We elucidate the topological features of the entanglement entropy of a region in two dimensional quantum systems in a topological phase with a finite correlation length $\xi$. Firstly, we suggest that simpler reduced quantities, related to the von Neumann entropy, could be defined to compute the topological entropy. We use our methods to compute the entanglement entropy for the ground state wave function of a quantum eight-vertex model in its topological phase, and show that a finite correlation length adds corrections of the same order as the topological entropy which come from sharp features of the boundary of the region under study. We also calculate the topological entropy for the ground state of the quantum dimer model on a triangular lattice by using a mapping to a loop model. The topological entropy of the state is determined by loop configurations with a non-trivial winding number around the region under study. Finally, we consider extensions of the Kitaev wave function, which incorporate the effects of electric and magnetic charge fluctuations, and use it to investigate the stability of the topological phase by calculating the topological entropy.Comment: 17 pages, 4 figures, published versio

A laboratory investigation on an undisturbed silty sand from a slope prone to landsliding

A laboratory investigation is presented for undisturbed samples of a silty sand under saturated conditions. The soil was sampled from test pits south of Rüdlingen in North–East Switzerland, where a landslide triggering experiment was carried out on a steep forest slope. The aim of the work was to characterise the behaviour of the soil in triaxial tests, in the light of the possible failure mechanisms of the slope. Conventional drained and undrained triaxial tests were conducted to detect critical state conditions as well as peak shear strength as a function of confining pressure. Soil specimens were also exposed to stress paths simulating in situ water pressure increase to study the stress–strain response and to enhance the ability to predict failure conditions more accurately in the future. Possible unstable response along the stress paths analysed was investigated by means of second order work and strain acceleration. The results show that temporary unstable conditions may be encountered for this soil at stress ratios below ultimate failure and even below critical state line, depending on void ratio, drainage conditions and time dependent compressibility. A modified state parameter is explored as a potentially useful tool to discriminate conditions leading to eventual collapse