Non-equilibrium Thermodynamics of Spacetime: the Role of Gravitational Dissipation

In arXiv:gr-qc/9504004 it was shown that the Einstein equation can be derived as a local constitutive equation for an equilibrium spacetime thermodynamics. More recently, in the attempt to extend the same approach to the case of $f(R)$ theories of gravity, it was found that a non-equilibrium setting is indeed required in order to fully describe both this theory as well as classical GR (arXiv:gr-qc/0602001). Here, elaborating on this point, we show that the dissipative character leading to a non-equilibrium spacetime thermodynamics is actually related -- both in GR as well as in $f(R)$ gravity -- to non-local heat fluxes associated with the purely gravitational/internal degrees of freedom of the theory. In particular, in the case of GR we show that the internal entropy production term is identical to the so called tidal heating term of Hartle-Hawking. Similarly, for the case of $f(R)$ gravity, we show that dissipative effects can be associated with the generalization of this term plus a scalar contribution whose presence is clearly justified within the scalar-tensor representation of the theory. Finally, we show that the allowed gravitational degrees of freedom can be fixed by the kinematics of the local spacetime causal structure, through the specific Equivalence Principle formulation. In this sense, the thermodynamical description seems to go beyond Einstein's theory as an intrinsic property of gravitation.Comment: 13 pages, 1 figur

Entropy and Topology for Gravitational Instantons

In this work a relation between topology and thermodynamical features of gravitational instantons is shown. The expression for the Euler characteristic, through the Gauss-Bonnet integral, and the one for the entropy of gravitational instantons are proposed in a form that makes the relation between them self-evident. A new formulation of the Bekenstein-Hawking formula, where the entropy and the Euler characteristic are related by $S=\chi A/8$, is obtained. This formula provides the correct results for a wide class of gravitational instantons described by both spherically and axially symmetric metrics.Comment: 25 pages, RevTeX, accepted for publication in Phys. Rev.

Dynamic distributed clustering in wireless sensor networks via Voronoi tessellation control

This paper presents two dynamic and distributed clustering algorithms for Wireless Sensor Networks (WSNs). Clustering approaches are used in WSNs to improve the network lifetime and scalability by balancing the workload among the clusters. Each cluster is managed by a cluster head (CH) node. The first algorithm requires the CH nodes to be mobile: by dynamically varying the CH node positions, the algorithm is proved to converge to a specific partition of the mission area, the generalised Voronoi tessellation, in which the loads of the CH nodes are balanced. Conversely, if the CH nodes are fixed, a weighted Voronoi clustering approach is proposed with the same load-balancing objective: a reinforcement learning approach is used to dynamically vary the mission space partition by controlling the weights of the Voronoi regions. Numerical simulations are provided to validate the approaches

Sonoluminescence: Two-photon correlations as a test of thermality

In this Letter we propose a fundamental test for probing the thermal nature of the spectrum emitted by sonoluminescence. We show that two-photon correlations can in principle discriminate between real thermal light and the quasi-thermal squeezed-state photons typical of models based on the dynamic Casimir effect. Two-photon correlations provide a powerful experimental test for various classes of sonoluminescence models.Comment: 6 pages, revtex 3; revised to include more discussion of finite volume effects; physics conclusions unchanged; to appear in Physics Letters

On pseudo-bialgebras

We study pseudoalgebras from the point of view of pseudo-dual of classical Lie coalgebra structures. We define the notions of Lie H-coalgebra and Lie pseudo-bialgebra. We obtain the analog of the CYBE, the Manin triples and Drinfeld's double for Lie pseudo-bialgebras. We also get a natural description of the annihilation algebra associated to a pseudoalgebra as a convolution algebra, clarifying this constructions in the theory of pseudoalgebras.Comment: arXiv admin note: substantial text overlap with arXiv:math/000712

Perturbative superluminal censorship and the null energy condition

We argue that ``effective'' superluminal travel, potentially caused by the tipping over of light cones in Einstein gravity, is always associated with violations of the null energy condition (NEC). This is most easily seen by working perturbatively around Minkowski spacetime, where we use linearized Einstein gravity to show that the NEC forces the light cones to contract (narrow). Given the NEC, the Shapiro time delay in any weak gravitational field is always a delay relative to the Minkowski background, and never an advance. Furthermore, any object travelling within the lightcones of the weak gravitational field is similarly delayed with respect to the minimum traversal time possible in the background Minkowski geometry.Comment: 5 pages. Uses AIP proceedings style (aipproc.sty). To appear in the Proceedings of the Eighth Canadian Conference on General Relativity and Relativistic Astrophysics. (McGill University, Montreal, June 1999). To be published by AIP Pres