Grand canonical ensemble in generalized thermostatistics

We study the grand-canonical ensemble with a fluctuating number of degrees of freedom in the context of generalized thermostatistics. Several choices of grand-canonical entropy functional are considered. The ideal gas is taken as an example.Comment: 14 pages, no figure

Tsallis statistics generalization of non-equilibrium work relations

We use third constraint formulation of Tsallis statistics and derive the $q$-statistics generalization of non-equilibrium work relations such as the Jarzynski equality and the Crooks fluctuation theorem which relate the free energy differences between two equilibrium states and the work distribution of the non-equilibrium processes.Comment: 5 page

Fast Algorithms for Constructing Maximum Entropy Summary Trees

Karloff? and Shirley recently proposed summary trees as a new way to visualize large rooted trees (Eurovis 2013) and gave algorithms for generating a maximum-entropy k-node summary tree of an input n-node rooted tree. However, the algorithm generating optimal summary trees was only pseudo-polynomial (and worked only for integral weights); the authors left open existence of a olynomial-time algorithm. In addition, the authors provided an additive approximation algorithm and a greedy heuristic, both working on real weights. This paper shows how to construct maximum entropy k-node summary trees in time O(k^2 n + n log n) for real weights (indeed, as small as the time bound for the greedy heuristic given previously); how to speed up the approximation algorithm so that it runs in time O(n + (k^4/eps?) log(k/eps?)), and how to speed up the greedy algorithm so as to run in time O(kn + n log n). Altogether, these results make summary trees a much more practical tool than before.Comment: 17 pages, 4 figures. Extended version of paper appearing in ICALP 201

Entanglement of a microcanonical ensemble

We replace time-averaged entanglement by ensemble-averaged entanglement and derive a simple expression for the latter. We show how to calculate the ensemble average for a two-spin system and for the Jaynes-Cummings model. In both cases the time-dependent entanglement is known as well so that one can verify that the time average coincides with the ensemble average.Comment: 10 page

The quantum double well anharmonic oscillator in an external field

The aim of this paper is twofold. First of all, we study the behaviour of the lowest eigenvalues of the quantum anharmonic oscillator under influence of an external field. We try to understand this behaviour using perturbation theory and compare the results with numerical calculations. This brings us to the second aim of selecting the best method to carry out the numerical calculations accurately.Comment: 9 pages, 6 figure

Covariance systems

We introduce new definitions of states and of representations of covariance systems. The GNS-construction is generalized to this context. It associates a representation with each state of the covariance system. Next, states are extended to states of an appropriate covariance algebra. Two applications are given. We describe a nonrelativistic quantum particle, and we give a simple description of the quantum spacetime model introduced by Doplicher et al.Comment: latex with ams-latex, 23 page

Extension of Information Geometry to Non-statistical Systems: Some Examples

Our goal is to extend information geometry to situations where statistical modeling is not obvious. The setting is that of modeling experimental data. Quite often the data are not of a statistical nature. Sometimes also the model is not a statistical manifold. An example of the former is the description of the Bose gas in the grand canonical ensemble. An example of the latter is the modeling of quantum systems with density matrices. Conditional expectations in the quantum context are reviewed. The border problem is discussed: through conditioning the model point shifts to the border of the differentiable manifold.Comment: 8 pages, to be published in the proceedings of GSI2015, Lecture Notes in Computer Science, Springe

The q-exponential family in statistical physics

The notion of generalised exponential family is considered in the restricted context of nonextensive statistical physics. Examples are given of models belonging to this family. In particular, the q-Gaussians are discussed and it is shown that the configurational probability distributions of the microcanonical ensemble belong to the q-exponential family.Comment: 18 pages, 4 figures, proceedings of SigmaPhi 200

Quantum and Fisher Information from the Husimi and Related Distributions

The two principal/immediate influences -- which we seek to interrelate here -- upon the undertaking of this study are papers of Zyczkowski and Slomczy\'nski (J. Phys. A 34, 6689 [2001]) and of Petz and Sudar (J. Math. Phys. 37, 2262 [1996]). In the former work, a metric (the Monge one, specifically) over generalized Husimi distributions was employed to define a distance between two arbitrary density matrices. In the Petz-Sudar work (completing a program of Chentsov), the quantum analogue of the (classically unique) Fisher information (montone) metric of a probability simplex was extended to define an uncountable infinitude of Riemannian (also monotone) metrics on the set of positive definite density matrices. We pose here the questions of what is the specific/unique Fisher information metric for the (classically-defined) Husimi distributions and how does it relate to the infinitude of (quantum) metrics over the density matrices of Petz and Sudar? We find a highly proximate (small relative entropy) relationship between the probability distribution (the quantum Jeffreys' prior) that yields quantum universal data compression, and that which (following Clarke and Barron) gives its classical counterpart. We also investigate the Fisher information metrics corresponding to the escort Husimi, positive-P and certain Gaussian probability distributions, as well as, in some sense, the discrete Wigner pseudoprobability. The comparative noninformativity of prior probability distributions -- recently studied by Srednicki (Phys. Rev. A 71, 052107 [2005]) -- formed by normalizing the volume elements of the various information metrics, is also discussed in our context.Comment: 27 pages, 10 figures, slight revisions, to appear in J. Math. Phy

The use of acoustic seafloor backscatter measurements for quantitative and qualitative characterization of methane seep areas

During the 2003 and 2004 cruises of the EC project CRIMEA almost 3000 active methane seeps were detected with an adapted scientific split-beam echosounder in the Dnepr paleo-delta area in the NW Black Sea (Naudts et al., in press). The seeps are widely, but not randomly, distributed over the transition zone between the continental shelf and slope, in water depths of 66 to 825 m. The highest concentration of seeps occurs on the shelf, in water depths of 80 to 95 m. Here, the location of the seeps is controlled by the underlying geology (filled channels) and seepage is characterized by the presence of pockmarks and high acoustic seafloor backscatter, visible on both multibeam and side-scan sonar data.Since seep detection during the CRIMEA cruises was performed independently but simultaneously with the multibeam and side-scan sonar recordings, these datasets possess a great potential for quantitative and qualitative analyses of acoustic seafloor backscatter in relation to the seep locations. Our analyses are further sustained by visual observations, high-resolution 5 kHz seismic data and sediment samples from gravity and multi-coring.For this study we selected an area of 37 km2 on the shelf.Within this area the normalized multibeam backscatter values ranges from -28.32 dB to 20.42 dB. After eliminating high-backscatter values caused by high topographic gradients, all seep positions within this area correspond to backscatter values of more than -2.89 dB and have a standard normal distribution. Furthermore, no seeps occur at locations characterized by the highest backscatter values. Within the area, 99.3 % of the seeps correspond to backscatter values ranging between -1.39 and 4.60 dB.These data indicate that actively bubbling seeps do not necessarily correspond to the highest backscatter values as would be expected; they rather surround the highbackscatter areas. This is also clear from visual observations in which bubbles are seen to emanate at the perimeter of white Beggiatoa mats. Since Beggiatoa mats are commonly associated with the precipitation of authigenic carbonates formed via AOM, these carbonates are very likely to be the cause of the higher backscatter values. Sediment samples and visual observation also indicated that areas corresponding to higher backscatter values are characterised by more shell material in the first 5-10 cm of the seabed.Also pockmarks are characterised by typical backscatter patterns. Better evolved, deeper, pockmarks are characterised by higher backscatter values and the seep activity is lower than at shallow pockmarks, which are often active bubbling. This could be explained by some sort of self-sealing of these seeps, as postulated by Hovland (2002).All these observations at the seafloor are clearly a result of the underlying geology where fluid migration is focussed to the sides of filled paleo-channels. The seismic data show the presence of a distinct “gas front” that locally domes up to the seafloor. These areas of gas front updoming on the shelf are characterised by seeps, higher backscatter values, Beggiatoa mats and pockmarks