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Entanglement entropy is a measure of the degree of correlation between subspaces of a given state. When considering the vacuum state of quantum field theory, the entanglement entropy of such a state is usually associated with a partitioning of space into an interior and exterior, the entanglement entropy measuring the degree of correlation along the interface in the vacuum. 

Since the vacuum is invariant under boosts one expects that the entanglement entropy will also be invariant under boosts and this is, indeed, usually the case. However, for certain quantum field theories, boost invariance can be anomalous. An anomalous symmetry is a symmetry which is broken by quantum mechanical effects. Such anomalies typically arise if the theory possesses an imbalance of chiral fermions. 

In a recent paper, Amos Yarom and Tatsuma Nishioka, have shown that in the presence of anomalies the entanglement entropy is not invariant under boosts. Moreover, the non boost invariance of the entanglement entropy can be characterised in a unique way such that its behaviour can be computed independently of the detailed description of the system. In this sense the contribution of anomalies to entanglement entropy can be considered to be universal.

Noether’s theorem relates symmetries to conservation laws. In a classical theory, a symmetry of the action implies an associated conserved charge. This relation does not necessarily hold in a quantum theory. Indeed, a the violation of what would seem like a symmetry of the theory due to quantum effects is referred to as an anomaly. In a recent paper, E. Shaverin and A. Yarom have argued that such a quantum mechanical effect should be made visible at a macroscopic level. In particular, they consider a gas of particles whose dynamics are governed by an anomalous theory, and which is trapped inside a spherical rotating shell. If the gas is instantaneously released from the shell then the anomaly would force the emission of the gas to be directional which implies, via momentum conservation that the shell will be propelled forward. This is an instance were a subtle quantum mechanical effect has a large scale manifestation.

One of the characteristics of a relativistic fluid is its shear viscosity which describes the response of the fluid to shear flow. Over the last ten years the shear viscosity of relativistic fluids whose underlying degrees of freedom are described by gauge-theories has been extensively studied. In particular, the shear viscosity of a certain class of gauge theory fluids which are described by a holographic dual has been shown to be proportional to the entropy density of such fluids with a universal proportionality constant. The proof of this universality relies on the system being isotropic, homogenous and thermally equilibrated. In a recent paper, the shear viscosity to entropy density ratio has been studied for thermally equilibrated and spatially modulated phases. It was shown that in such phases the shear viscosity is modulated while the entropy density is not, leading to a non universal ratio.

Transport properties of fluids characterize the way fluids respond to perturbations. For instance, the shear viscosity of a fluid can be thought of as describing its (linear) response to metric perturbations, electric conductivity describes the response of a fluid to an external electric field etc. If the underlying theory describing a fluid is anomalous, i.e., its symmetries are spoiled by quantum effects, then the fluid will respond non trivially to vorticity and an external (flavor) magnetic field. The study of the anomalous response of normal fluids to perturbations has been extensively studied in the literature.

Superfluids are special types of fluids in which extra quantum excitations modify the fluid behavior so that it allows for dissipationless configurations. The standard analysis of the relation between anomalies and transport does not give clear predictions when applied to superfluids. In a recent paper I. Amado, N. Lisker and A. Yarom have shown that for particular kinds of superfluids—those that have an alternate (holographic) description, the transport coefficients associated with vorticity and a magnetic field are fixed uniquely by the anomaly. It remains to be seen if this somewhat mysterious relation holds for all types of superfluids or is a unique features of holographic ones.

While statistical mechanics provides us with powerful tools to analyze systems in equi- librium, most of the world around us is far from this idealized situation. Near thermal equilibrium, one can use hydrodynamics to analyze the dynamics of small, long wavelength fluctuations. But to understand far from equilibrium physics is a notoriously challenging problem. An interesting yet potentially tractable class of non-equilibrium configurations is represented by steady state flows. Examples of steady state flows are an electric current in a conductor driven by an external electric field or a heat current driven by a temperature gradient. These configurations can be described by a time-independent configuration, but neither of these corresponds to equilibrium. In both cases entropy is produced constantly and needs to be absorbed by the battery or heat bath in order to maintain the steady flow.

In a recent paper H. Chang, A. Karch and A. Yarom have constructed an ansatz which describes a particular type of such a steady state configuration. The particular solution which has been constructed is such that, in conformal theories, the properties of the steady-state heat current is independent of the parameters of the theory and is, in this sense, universal. Various indications as to the validity of this ansatz have been given, but it has not been rigorously proven or tested very robustly.