New Types of Thermodynamics from (1+1)(1+1)-Dimensional Black Holes

For normal thermodynamic systems superadditivity $\S$, homogeneity \H and concavity \C of the entropy hold, whereas for $(3+1)$-dimensional black holes the latter two properties are violated. We show that $(1+1)$-dimensional black holes exhibit qualitatively new types of thermodynamic behaviour, discussed here for the first time, in which \C always holds, \H is always violated and $\S$ may or may not be violated, depending of the magnitude of the black hole mass. Hence it is now seen that neither superadditivity nor concavity encapsulate the meaning of the second law in all situations.Comment: WATPHYS-TH93/05, Latex, 10 pgs. 1 figure (available on request), to appear in Class. Quant. Gra

Statistical Mechanics of Relativistic One-Dimensional Self-Gravitating Systems

We consider the statistical mechanics of a general relativistic one-dimensional self-gravitating system. The system consists of $N$-particles coupled to lineal gravity and can be considered as a model of $N$ relativistically interacting sheets of uniform mass. The partition function and one-particle distitrubion functions are computed to leading order in $1/c$ where $c$ is the speed of light; as $c\to\infty$ results for the non-relativistic one-dimensional self-gravitating system are recovered. We find that relativistic effects generally cause both position and momentum distribution functions to become more sharply peaked, and that the temperature of a relativistic gas is smaller than its non-relativistic counterpart at the same fixed energy. We consider the large-N limit of our results and compare this to the non-relativistic case.Comment: latex, 60 pages, 22 figure

Decoherent Histories Quantum Mechanics with One 'Real' Fine-Grained History

Decoherent histories quantum theory is reformulated with the assumption that there is one "real" fine-grained history, specified in a preferred complete set of sum-over-histories variables. This real history is described by embedding it in an ensemble of comparable imagined fine-grained histories, not unlike the familiar ensemble of statistical mechanics. These histories are assigned extended probabilities, which can sometimes be negative or greater than one. As we will show, this construction implies that the real history is not completely accessible to experimental or other observational discovery. However, sufficiently and appropriately coarse-grained sets of alternative histories have standard probabilities providing information about the real fine-grained history that can be compared with observation. We recover the probabilities of decoherent histories quantum mechanics for sets of histories that are recorded and therefore decohere. Quantum mechanics can be viewed as a classical stochastic theory of histories with extended probabilities and a well-defined notion of reality common to all decoherent sets of alternative coarse-grained histories.Comment: 11 pages, one figure, expanded discussion and acknowledgment

An experimental study of intermodulation effects in an atomic fountain frequency standard

The short-term stability of passive atomic frequency standards, especially in pulsed operation, is often limited by local oscillator noise via intermodulation effects. We present an experimental demonstration of the intermodulation effect on the frequency stability of a continuous atomic fountain clock where, under normal operating conditions, it is usually too small to observe. To achieve this, we deliberately degrade the phase stability of the microwave field interrogating the clock transition. We measure the frequency stability of the locked, commercial-grade local oscillator, for two modulation schemes of the microwave field: square-wave phase modulation and square-wave frequency modulation. We observe a degradation of the stability whose dependence with the modulation frequency reproduces the theoretical predictions for the intermodulation effect. In particular no observable degradation occurs when this frequency equals the Ramsey linewidth. Additionally we show that, without added phase noise, the frequency instability presently equal to 2x10-13 at 1s, is limited by atomic shot-noise and therefore could be reduced were the atomic flux increased

Symmetry Breaking Using Value Precedence

We present a comprehensive study of the use of value precedence constraints to break value symmetry. We first give a simple encoding of value precedence into ternary constraints that is both efficient and effective at breaking symmetry. We then extend value precedence to deal with a number of generalizations like wreath value and partial interchangeability. We also show that value precedence is closely related to lexicographical ordering. Finally, we consider the interaction between value precedence and symmetry breaking constraints for variable symmetries.Comment: 17th European Conference on Artificial Intelligenc

Proteomics of Cytochrome c Oxidase-Negative versus -Positive Muscle Fiber Sections in Mitochondrial Myopathy

The mosaic distribution of cytochrome c oxidase(+) (COX+) and COX - muscle fibers in mitochondrial disorders allows the sampling of fibers with compensated and decompensated mitochondrial function from the same individual. We apply laser capture microdissection to excise individual COX+ and COX- fibers from the biopsies of mitochondrial myopathy patients. Using mass spectrometry-based proteomics, we quantify >4,000 proteins per patient. While COX+ fibers show a higher expression of respiratory chain components, COX- fibers display protean adaptive responses, including upregulation of mitochondrial ribosomes, translation proteins, and chaperones. Upregulated proteins include C1QBP, required for mitoribosome formation and protein synthesis, and STOML2, which organizes cardiolipin-enriched microdomains and the assembly of respiratory supercomplexes. Factoring in fast/slow fiber type, COX (-) slow fibers show a compensatory upregulation of beta-oxidation, the AAA(+) protease AFG3L1, and the OPA1-dependent cristae remodeling program. These findings reveal compensatory mechanisms in muscle fibers struggling with energy shortage and metabolic stress

Two-dimensional gravitation and Sine-Gordon-Solitons

Some aspects of two-dimensional gravity coupled to matter fields, especially to the Sine-Gordon-model are examined. General properties and boundary conditions of possible soliton-solutions are considered. Analytic soliton-solutions are discovered and the structure of the induced space-time geometry is discussed. These solutions have interesting features and may serve as a starting point for further investigations.Comment: 23 pages, latex, references added, to appear in Phys.Rev.

Self-completeness and spontaneous dimensional reduction

A viable quantum theory of gravity is one of the biggest challenges facing physicists. We discuss the confluence of two highly expected features which might be instrumental in the quest of a finite and renormalizable quantum gravity -- spontaneous dimensional reduction and self-completeness. The former suggests the spacetime background at the Planck scale may be effectively two-dimensional, while the latter implies a condition of maximal compression of matter by the formation of an event horizon for Planckian scattering. We generalize such a result to an arbitrary number of dimensions, and show that gravity in higher than four dimensions remains self-complete, but in lower dimensions it is not. In such a way we established an "exclusive disjunction" or "exclusive or" (XOR) between the occurrence of self-completeness and dimensional reduction, with the goal of actually reducing the unknowns for the scenario of the physics at the Planck scale. Potential phenomenological implications of this result are considered by studying the case of a two-dimensional dilaton gravity model resulting from dimensional reduction of Einstein gravity.Comment: 12 pages, 3 figures; v3: final version in press on Eur. Phys. J. Plu

N-body Gravity and the Schroedinger Equation

We consider the problem of the motion of $N$ bodies in a self-gravitating system in two spacetime dimensions. We point out that this system can be mapped onto the quantum-mechanical problem of an N-body generalization of the problem of the H$_{2}^{+}$ molecular ion in one dimension. The canonical gravitational N-body formalism can be extended to include electromagnetic charges. We derive a general algorithm for solving this problem, and show how it reduces to known results for the 2-body and 3-body systems.Comment: 15 pages, Latex, references added, typos corrected, final version that appears in CQ

Escape path complexity and its context dependency in Pacific blue-eyes (Pseudomugil signifer)

The escape trajectories animals take following a predatory attack appear to show high degrees of apparent 'randomness' - a property that has been described as 'protean behaviour'. Here we present a method of quantifying the escape trajectories of individual animals using a path complexity approach. When fish (Pseudomugil signifer) were attacked either on their own or in groups, we find that an individual's path rapidly increases in entropy (our measure of complexity) following the attack. For individuals on their own, this entropy remains elevated (indicating a more random path) for a sustained period (10 seconds) after the attack, whilst it falls more quickly for individuals in groups. The entropy of the path is context dependent. When attacks towards single fish come from greater distances, a fish's path shows less complexity compared to attacks that come from short range. This context dependency effect did not exist, however, when individuals were in groups. Nor did the path complexity of individuals in groups depend on a fish's local density of neighbours. We separate out the components of speed and direction changes to determine which of these components contributes to the overall increase in path complexity following an attack. We found that both speed and direction measures contribute similarly to an individual's path's complexity in absolute terms. Our work highlights the adaptive behavioural tactics that animals use to avoid predators and also provides a novel method for quantifying the escape trajectories of animals.Comment: 9 page