Generalized rotating-wave approximation for arbitrarily large coupling

A generalized version of the rotating-wave approximation for the single-mode spin-boson Hamiltonian is presented. It is shown that performing a simple change of basis prior to eliminating the off-resonant terms results in a significantly more accurate expression for the energy levels of the system. The generalized approximation works for all values of the coupling strength and for a wide range of detuning values, and may find applications in solid-state experiments.Comment: 4 pages, 2 figs, REVTeX

Microcanonical Origin of the Maximum Entropy Principle for Open Systems

The canonical ensemble describes an open system in equilibrium with a heat bath of fixed temperature. The probability distribution of such a system, the Boltzmann distribution, is derived from the uniform probability distribution of the closed universe consisting of the open system and the heat bath, by taking the limit where the heat bath is much larger than the system of interest. Alternatively, the Boltzmann distribution can be derived from the Maximum Entropy Principle, where the Gibbs-Shannon entropy is maximized under the constraint that the mean energy of the open system is fixed. To make the connection between these two apparently distinct methods for deriving the Boltzmann distribution, it is first shown that the uniform distribution for a microcanonical distribution is obtained from the Maximum Entropy Principle applied to a closed system. Then I show that the target function in the Maximum Entropy Principle for the open system, is obtained by partial maximization of Gibbs-Shannon entropy of the closed universe over the microstate probability distributions of the heat bath. Thus, microcanonical origin of the Entropy Maximization procedure for an open system, is established in a rigorous manner, showing the equivalence between apparently two distinct approaches for deriving the Boltzmann distribution. By extending the mathematical formalism to dynamical paths, the result may also provide an alternative justification for the principle of path entropy maximization as well.Comment: 12 pages, no figur

A link between the maximum entropy approach and the variational entropy form

The maximum entropy approach operating with quite general entropy measure and constraint is considered. It is demonstrated that for a conditional or parametrized probability distribution $f(x|\mu)$ there is a "universal" relation among the entropy rate and the functions appearing in the constraint. It is shown that the recently proposed variational formulation of the entropic functional can be obtained as a consequence of this relation, that is from the maximum entropy principle. This resolves certain puzzling points appeared in the variational approach

Generalized molecular chaos hypothesis and H-theorem: Problem of constraints and amendment of nonextensive statistical mechanics

Quite unexpectedly, kinetic theory is found to specify the correct definition of average value to be employed in nonextensive statistical mechanics. It is shown that the normal average is consistent with the generalized Stosszahlansatz (i.e., molecular chaos hypothesis) and the associated H-theorem, whereas the q-average widely used in the relevant literature is not. In the course of the analysis, the distributions with finite cut-off factors are rigorously treated. Accordingly, the formulation of nonextensive statistical mechanics is amended based on the normal average. In addition, the Shore-Johnson theorem, which supports the use of the q-average, is carefully reexamined, and it is found that one of the axioms may not be appropriate for systems to be treated within the framework of nonextensive statistical mechanics.Comment: 22 pages, no figures. Accepted for publication in Phys. Rev.

Selective Control of the Symmetric Dicke Subspace in Trapped Ions

We propose a method of manipulating selectively the symmetric Dicke subspace in the internal degrees of freedom of N trapped ions. We show that the direct access to ionic-motional subspaces, based on a suitable tuning of motion-dependent AC Stark shifts, induces a two-level dynamics involving previously selected ionic Dicke states. In this manner, it is possible to produce, sequentially and unitarily, ionic Dicke states with increasing excitation number. Moreover, we propose a probabilistic technique to produce directly any ionic Dicke state assuming suitable initial conditions.Comment: 5 pages and 1 figure. New version with minor changes and added references. Accepted in Physical Review

Comparing Infrared Dirac-Born-Infeld Brane Inflation to Observations

We compare the Infrared Dirac-Born-Infeld (IR DBI) brane inflation model to observations using a Bayesian analysis. The current data cannot distinguish it from the \LambdaCDM model, but is able to give interesting constraints on various microscopic parameters including the mass of the brane moduli potential, the fundamental string scale, the charge or warp factor of throats, and the number of the mobile branes. We quantify some distinctive testable predictions with stringy signatures, such as the large non-Gaussianity, and the large, but regional, running of the spectral index. These results illustrate how we may be able to probe aspects of string theory using cosmological observations.Comment: 54 pages, 13 figures. v2: non-Gaussianity constraint has been applied to the model; parameter constraints have tightened significantly, conclusions unchanged. References added; v3, minor revision, PRD versio

Rules for transition rates in nonequilibrium steady states

Just as transition rates in a canonical ensemble must respect the principle of detailed balance, constraints exist on transition rates in driven steady states. I derive those constraints, by maximum information-entropy inference, and apply them to the steady states of driven diffusion and a sheared lattice fluid. The resulting ensemble can potentially explain nonequilibrium phase behaviour and, for steady shear, gives rise to stress-mediated long-range interactions.Comment: 4 pages. To appear in Physical Review Letter

Information Theory based on Non-additive Information Content

We generalize the Shannon's information theory in a nonadditive way by focusing on the source coding theorem. The nonadditive information content we adopted is consistent with the concept of the form invariance structure of the nonextensive entropy. Some general properties of the nonadditive information entropy are studied, in addition, the relation between the nonadditivity $q$ and the codeword length is pointed out.Comment: 9 pages, no figures, RevTex, accepted for publication in Phys. Rev. E(an error in proof of theorem 1 was corrected, typos corrected

Incomplete quantum process tomography and principle of maximal entropy

The main goal of this paper is to extend and apply the principle of maximum entropy (MaxEnt) to incomplete quantum process estimation tasks. We will define a so-called process entropy function being the von Neumann entropy of the state associated with the quantum process via Choi-Jamiolkowski isomorphism. It will be shown that an arbitrary process estimation experiment can be reformulated in a unified framework and MaxEnt principle can be consistently exploited. We will argue that the suggested choice for the process entropy satisfies natural list of properties and it reduces to the state MaxEnt principle, if applied to preparator devices.Comment: 8 pages, comments welcome, references adde

Properties of a non-equilibrium heat bath

At equilibrium, a fluid element, within a larger heat bath, receives random impulses from the bath. Those impulses, which induce stochastic transitions in the system (the fluid element), respect the principle of detailed balance, because the bath is also at equilibrium. Under continuous shear, the fluid element adopts a non-equilibrium steady state. Because the surrounding bath of fluid under shear is also in a non-equilibrium steady state, the system receives stochastic impulses with a non-equilibrium distribution. Those impulses no longer respect detailed balance, but are nevertheless constrained by rules. The rules in question, which are applicable to a wide sub-class of driven steady states, were recently derived [R. M. L. Evans, Phys. Rev. Lett. {\bf 92}, 150601 (2004); J. Phys. A: Math. Gen. {\bf 38}, 293 (2005)] using information-theoretic arguments. In the present paper, we provide a more fundamental derivation, based on the uncontroversial, non-Bayesian interpretation of probabilities as simple ratios of countable quantities. We apply the results to some simple models of interacting particles, to investigate the nature of forces that are mediated by a non-equilibrium noise-source such as a fluid under shear.Comment: 14 pages, 7 figure