Typicality in spin network states of quantum geometry

In this work, we extend the so-called typicality approach, originally formulated in statistical mechanics contexts, to $SU(2)$-invariant spin-network states. Our results do not depend on the physical interpretation of the spin network; however, they are mainly motivated by the fact that spin-network states can describe states of quantum geometry, providing a gauge-invariant basis for the kinematical Hilbert space of several background-independent approaches to quantum gravity. The first result is, by itself, the existence of a regime in which we show the emergence of a typical state. We interpret this as the proof that in that regime there are certain (local) properties of quantum geometry which are "universal". Such a set of properties is heralded by the typical state, of which we give the explicit form. This is our second result. In the end, we study some interesting properties of the typical state, proving that the area law for the entropy of a surface must be satisfied at the local level, up to logarithmic corrections which we are able to bound.Comment: Typos and mistakes fixe

Statistical mechanics of covariant systems with multi-fingered time

Recently, in [Class. Quantum Grav. 33 (2016) 045005], the authors proposed a new approach extending the framework of statistical mechanics to reparametrization-invariant systems with no additional gauges. In this work, the approach is generalized to systems defined by more than one Hamiltonian constraints (multi-fingered time). We show how well known features as the Ehrenfest- Tolman effect and the J\"uttner distribution for the relativistic gas can be consistently recovered from a covariant approach in the multi-fingered framework. Eventually, the crucial role played by the interaction in the definition of a global notion of equilibrium is discussed.Comment: 5 pages, 2 figure

On the fate of the Hoop Conjecture in quantum gravity

We consider a closed region $R$ of 3d quantum space modeled by $SU(2)$ spin-networks. Using the concentration of measure phenomenon we prove that, whenever the ratio between the boundary $\partial R$ and the bulk edges of the graph overcomes a finite threshold, the state of the boundary is always thermal, with an entropy proportional to its area. The emergence of a thermal state of the boundary can be traced back to a large amount of entanglement between boundary and bulk degrees of freedom. Using the dual geometric interpretation provided by loop quantum gravity, we interprete such phenomenon as a pre-geometric analogue of Thorne's "Hoop conjecture", at the core of the formation of a horizon in General Relativity.Comment: 7 pages, 2 figures, minor improvement

Adapting to extreme environments: can coral reefs adapt to climate change?

Reef-building corals throughout the world have an annual value of tens of billions of dollars, yet they are being degraded at an increasing rate by many anthropogenic and environmental factors. Despite this, some reefs show resilience to such extreme environmental changes. This review shows how techniques in computational modelling, genetics, and transcriptomics are being used to unravel the complexity of coral reef ecosystems, to try and understand if they can adapt to new and extreme environments. Considering the ambitious climate targets of the Paris Agreement to limit global warming to 2°C, with aspirations of even 1.5°C, questions arise on how to achieve this. Geoengineering may be necessary if other avenues fail, although global governance issues need to play a key role. Development of large and effective coral refugia and marine protected areas is necessary if we are not to lose this vital resource for us all