Goffredo Chirco

Spacetime thermodynamics without hidden degrees of freedom

A celebrated result by Jacobson is the derivation of Einsteins equations from Unruhs temperature, the Bekenstein-Hawking entropy and the Clausius relation. This has been repeatedly taken as evidence for an interpretation of Einsteins equations as equations of state for unknown degrees of freedom underlying the metric. We show that a different interpretation of Jacobson result is possible, which does not imply the existence of additional degrees of freedom, and follows only from the quantum properties of gravity. We introduce the notion of quantum gravitational Hadamard states, which give rise to the full local thermodynamics of gravity.

Reversible and Irreversible Spacetime Thermodynamics for General Brans-Dicke Theories

We derive the equations of motion for Palatini F(R) gravity by applying an entropy balance law TdS={delta}Q+{delta}N to the local Rindler wedge that can be constructed at each point of spacetime. Unlike previous results for metric F(R), there is no bulk viscosity term in the irreversible flux {delta}N. Both theories are equivalent to particular cases of Brans-Dicke scalar-tensor gravity. We show that the thermodynamical approach can be used ab initio also for this class of gravitational theories and it is able to provide both the metric and scalar equations of motion. In this case, the presence of an additional scalar degree of freedom and the requirement for it to be dynamical naturally imply a separate contribution from the scalar field to the heat flux {delta}Q. Therefore, the gravitational flux previously associated to a bulk viscosity term in metric F(R) turns out to be actually part of the reversible thermodynamics. Hence we conjecture that only the shear viscosity associated with Hartle-Hawking dissipation should be associated with irreversible thermodynamics.

Coupling and thermal equilibrium in general-covariant systems

A fully general-covariant formulation of statistical mechanics is still lacking. We take a step toward this theory by studying the meaning of statistical equilibrium for coupled, parametrized systems. We discuss how to couple parametrized systems. We express the thermalization hypothesis in a general-covariant context. This takes the form of vanishing of information flux. An interesting relation emerges between thermal equilibrium and gauge.

Fisher Metric, Geometric Entanglement and Spin Networks

Starting from recent results on the geometric formulation of quantum mechanics, we propose a new information geometric characterization of entanglement for spin network states in the context of quantum gravity. For the simple case of a single-link fixed graph (Wilson line), we detail the construction of a Riemannian Fisher metric tensor and a symplectic structure on the graph Hilbert space, showing how these encode the whole information about separability and entanglement. In particular, the Fisher metric defines an entanglement monotone which provides a notion of distance among states in the Hilbert space. In the maximally entangled gauge-invariant case, the entanglement monotone is proportional to a power of the area of the surface dual to the link thus supporting a connection between entanglement and the (simplicial) geometric properties of spin network states. We further extend such analysis to the study of nonlocal correlations between two nonadjacent regions of a generic spin network graph characterized by the bipartite unfolding of an intertwiner state. Our analysis confirms the interpretation of spin network bonds as a result of entanglement and to regard the same spin network graph as an information graph, whose connectivity encodes, both at the local and nonlocal level, the quantum correlations among its parts. This gives a further connection between entanglement and geometry.

Group Field theory and Tensor Networks: towards a Ryu-Takayanagi formula in full quantum gravity

We establish a dictionary between group field theory (thus, spin networks and random tensors) states and generalized random tensor networks. Then, we use this dictionary to compute the Renyi entropy of such states and recover the Ryu-Takayanagi formula, in two different cases corresponding to two different truncations/approximations, suggested by the established correspondence.

Statistical mechanics of reparametrization-invariant systems. It takes three to tango.

It is notoriously difficult to apply statistical mechanics to generally covariant systems, because the notions of time, energy and equilibrium are seriously modified in this context. We discuss the conditions under which weaker versions of these notions can be defined, sufficient for statistical mechanics. We focus on reparametrization-invariant systems without additional gauges. The key is to reconstruct statistical mechanics from the ergodic theorem. We find that a suitable split of the system into two non interacting components is sufficient for generalizing statistical mechanics. While equilibrium acquires sense only when the system admits a suitable split into three weakly interacting components ---roughly: a clock and two systems among which a generalization of energy is equi-partitioned. This allows the application of statistical mechanics and thermodynamics as an additivity condition of such generalized energy.

Ryu-Takayanagi Formula for Symmetric Random Tensor Networks

We consider the special case of random tensor networks (RTNs) endowed with gauge symmetry constraints on each tensor. We compute the Renyi entropy for such states and recover the Ryu-Takayanagi (RT) formula in the large-bond regime. The result provides first of all an interesting new extension of the existing derivations of the RT formula for RTNs. Moreover, this extension of the RTN formalism brings it in direct relation with (tensorial) group field theories (and spin networks), and thus provides new tools for realizing the tensor network/geometry duality in the context of background-independent quantum gravity, and for importing quantum gravity tools into tensor network research.

Hydrodynamics and viscosity in the Rindler spacetime

In the past year it has been shown that one can construct an approximate (d + 2) dimensional solution of the vacuum Einstein equations dual to a (d + 1) dimensional fluid satisfying the Navier-Stokes equations. The construction proceeds by perturbing the flat Rindler metric, subject to the boundary conditions of a non-singular causal horizon in the interior and a fixed induced metric on a given timelike surface r = rc in the bulk. We review this fluid-Rindler correspondence and show that the shear viscosity to entropy density ratio of the fluid on r = rc takes the universal value 1/4π both in Einstein gravity and in a wide class of higher curvature generalizations. Since the precise holographic duality for this spacetime is unknown, we propose a microscopic explanation for this viscosity based on the peculiar properties of quantum entanglement. Using a novel holographic Kubo formula in terms of a two-point function of the stress tensor of matter fields in the bulk, we calculate a shear viscosity and find ...