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

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

A one-dimensional model for theoretical analysis of single molecule experiments

In this paper we compare two polymer stretching experiments. The outcome of both experiments is a force-extension relation. We use a one-dimensional model to show that in general the two quantities are not equal. In certain limits, however, both force-extension relations coincide.Comment: 11 pages, 5 figure

Hilbert-Schmidt Separability Probabilities and Noninformativity of Priors

The Horodecki family employed the Jaynes maximum-entropy principle, fitting the mean (b_{1}) of the Bell-CHSH observable (B). This model was extended by Rajagopal by incorporating the dispersion (\sigma_{1}^2) of the observable, and by Canosa and Rossignoli, by generalizing the observable (B_{\alpha}). We further extend the Horodecki one-parameter model in both these manners, obtaining a three-parameter (b_{1},\sigma_{1}^2,\alpha) two-qubit model, for which we find a highly interesting/intricate continuum (-\infty < \alpha < \infty) of Hilbert-Schmidt (HS) separability probabilities -- in which, the golden ratio is featured. Our model can be contrasted with the three-parameter (b_{q}, \sigma_{q}^2,q) one of Abe and Rajagopal, which employs a q(Tsallis)-parameter rather than $\alpha$, and has simply q-invariant HS separability probabilities of 1/2. Our results emerge in a study initially focused on embedding certain information metrics over the two-level quantum systems into a q-framework. We find evidence that Srednicki's recently-stated biasedness criterion for noninformative priors yields rankings of priors fully consistent with an information-theoretic test of Clarke, previously applied to quantum systems by Slater.Comment: 26 pages, 12 figure

The Primary Energy Dependence of Backscattered Electron Images Up to 100 keV

The backscattered electron coefficient is known to be primarily dependent on the atomic number of the sample. If the atomic number increases, the backscattered electron coefficient increases, which results in a higher intensity in the backscattered electron image. The dependence of the primary electron energy is somewhat more complicated. Using photographic material (with composition AgBr-AgI), it is seen that the contrast in the backscattered electron image increases with the primary electron energy. Using three independent methods, based on image analysis techniques, it is shown that the difference between the backscattered electron coefficient of AgBr and AgI increases with the primary electron energy in the range from 40 to 100 keV

A two-parameter random walk with approximate exponential probability distribution

We study a non-Markovian random walk in dimension 1. It depends on two parameters eps_r and eps_l, the probabilities to go straight on when walking to the right, respectively to the left. The position x of the walk after n steps and the number of reversals of direction k are used to estimate eps_r and eps_l. We calculate the joint probability distribution p_n(x,k) in closed form and show that, approximately, it belongs to the exponential family.Comment: 12 pages, updated reference to companion paper cond-mat/060126

Stationary and dynamical properties of information entropies in nonextensive systems

The Tsallis entropy and Fisher information entropy (matrix) are very important quantities expressing information measures in nonextensive systems. Stationary and dynamical properties of the information entropies have been investigated in the $N$-unit coupled Langevin model subjected to additive and multiplicative white noise, which is one of typical nonextensive systems. We have made detailed, analytical and numerical study on the dependence of the stationary-state entropies on additive and multiplicative noise, external inputs, couplings and number of constitutive elements ($N$). By solving the Fokker-Planck equation (FPE) by both the proposed analytical scheme and the partial difference-equation method, transient responses of the information entropies to an input signal and an external force have been investigated. We have calculated the information entropies also with the use of the probability distribution derived by the maximum-entropy method (MEM), whose result is compared to that obtained by the FPE. The Cram\'{e}r-Rao inequality is shown to be expressed by the {\it extended} Fisher entropy, which is different from the {\it generalized} Fisher entropy obtained from the generalized Kullback-Leibler divergence in conformity with the Tsallis entropy. The effect of additive and multiplicative {\it colored} noise on information entropies is discussed also.Comment: 31 pages, 15 figures; changed text and figure

Darboux-integration of id\rho/dt=[H,f(\rho)]

A Darboux-type method of solving the nonlinear von Neumann equation $i\dot \rho=[H,f(\rho)]$, with functions $f(\rho)$ commuting with $\rho$, is developed. The technique is based on a representation of the nonlinear equation by a compatibility condition for an overdetermined linear system. von Neumann equations with various nonlinearities $f(\rho)$ are found to possess the so-called self-scattering solutions. To illustrate the result we consider the Hamiltonian $H$ of a one-dimensional harmonic oscillator and $f(\rho)=\rho^q-2\rho^{q-1}$ with arbitary real $q$. It is shown that self-scattering solutions possess the same asymptotics for all $q$ and that different nonlinearities may lead to effectively indistinguishable evolutions. The result may have implications for nonextensive statistics and experimental tests of linearity of quantum mechanics.Comment: revtex, 5 pages, 2 eps figures, submitted to Phys.Lett.A infinite-dimensional example is adde

Cavity-QED tests of representations of canonical commutation relations employed in field quantization

Various aspects of dissipative and nondissipative decoherence of Rabi oscillations are discussed in the context of field quantization in alternative representations of CCR. Theory is confronted with experiment, and a possibility of more conclusive tests is analyzed.Comment: Discussion of dissipative and nondissipative decoherence is included. Theory is now consistent with the existing data and predictions for new experiments are more reliabl