Universal efficiency at optimal work with Bayesian statistics

If the work per cycle of a quantum heat engine is averaged over an appropriate prior distribution for an external parameter $a$, the work becomes optimal at Curzon-Ahlborn efficiency. More general priors of the form $\Pi(a) \propto 1/a^{\gamma}$ yield optimal work at an efficiency which stays close to CA value, in particular near equilibrium the efficiency scales as one-half of the Carnot value. This feature is analogous to the one recently observed in literature for certain models of finite-time thermodynamics. Further, the use of Bayes' theorem implies that the work estimated with posterior probabilities also bears close analogy with the classical formula. These findings suggest that the notion of prior information can be used to reveal thermodynamic features in quantum systems, thus pointing to a new connection between thermodynamic behavior and the concept of information.Comment: revtex4, 5 pages, abstract changed and presentation improved; results unchanged. New result with Bayes Theorem adde

Expected Behavior of Quantum Thermodynamic Machines with Prior Information

We estimate the expected behavior of a quantum model of heat engine when we have incomplete information about external macroscopic parameters, like magnetic field controlling the intrinsic energy scales of the working medium. We explicitly derive the prior probability distribution for these unknown parameters, $a_i, (i=1,2)$. Based on a few simple assumptions, the prior is found to be of the form $\Pi(a_i) \propto 1/a_i$. By calculating the expected values of various physical quantities related to this engine, we find that the expected behavior of the quantum model exhibits thermodynamic-like features. This leads us to a surprising proposal that incomplete information quantified as appropriate prior distribution can lead us to expect classical thermodynamic behavior in quantum models.Comment: Revtex, 13 pages, 3 figures, revised version, new results added, accepted for Phys. Rev.

Might EPR particles communicate through a wormhole?

We consider the two-particle wave function of an Einstein-Podolsky-Rosen system, given by a two dimensional relativistic scalar field model. The Bohm-de Broglie interpretation is applied and the quantum potential is viewed as modifying the Minkowski geometry. In this way an effective metric, which is analogous to a black hole metric in some limited region, is obtained in one case and a particular metric with singularities appears in the other case, opening the possibility, following Holland, of interpreting the EPR correlations as being originated by an effective wormhole geometry, through which the physical signals can propagate.Comment: Corrected version, to appears in EP

The length of time's arrow

An unresolved problem in physics is how the thermodynamic arrow of time arises from an underlying time reversible dynamics. We contribute to this issue by developing a measure of time-symmetry breaking, and by using the work fluctuation relations, we determine the time asymmetry of recent single molecule RNA unfolding experiments. We define time asymmetry as the Jensen-Shannon divergence between trajectory probability distributions of an experiment and its time-reversed conjugate. Among other interesting properties, the length of time's arrow bounds the average dissipation and determines the difficulty of accurately estimating free energy differences in nonequilibrium experiments

Constructing smooth potentials of mean force, radial, distribution functions and probability densities from sampled data

In this paper a method of obtaining smooth analytical estimates of probability densities, radial distribution functions and potentials of mean force from sampled data in a statistically controlled fashion is presented. The approach is general and can be applied to any density of a single random variable. The method outlined here avoids the use of histograms, which require the specification of a physical parameter (bin size) and tend to give noisy results. The technique is an extension of the Berg-Harris method [B.A. Berg and R.C. Harris, Comp. Phys. Comm. 179, 443 (2008)], which is typically inaccurate for radial distribution functions and potentials of mean force due to a non-uniform Jacobian factor. In addition, the standard method often requires a large number of Fourier modes to represent radial distribution functions, which tends to lead to oscillatory fits. It is shown that the issues of poor sampling due to a Jacobian factor can be resolved using a biased resampling scheme, while the requirement of a large number of Fourier modes is mitigated through an automated piecewise construction approach. The method is demonstrated by analyzing the radial distribution functions in an energy-discretized water model. In addition, the fitting procedure is illustrated on three more applications for which the original Berg-Harris method is not suitable, namely, a random variable with a discontinuous probability density, a density with long tails, and the distribution of the first arrival times of a diffusing particle to a sphere, which has both long tails and short-time structure. In all cases, the resampled, piecewise analytical fit outperforms the histogram and the original Berg-Harris method.Comment: 14 pages, 15 figures. To appear in J. Chem. Phy

Extended Heat-Fluctuation Theorems for a System with Deterministic and Stochastic Forces

Heat fluctuations over a time \tau in a non-equilibrium stationary state and in a transient state are studied for a simple system with deterministic and stochastic components: a Brownian particle dragged through a fluid by a harmonic potential which is moved with constant velocity. Using a Langevin equation, we find the exact Fourier transform of the distribution of these fluctuations for all \tau. By a saddle-point method we obtain analytical results for the inverse Fourier transform, which, for not too small \tau, agree very well with numerical results from a sampling method as well as from the fast Fourier transform algorithm. Due to the interaction of the deterministic part of the motion of the particle in the mechanical potential with the stochastic part of the motion caused by the fluid, the conventional heat fluctuation theorem is, for infinite and for finite \tau, replaced by an extended fluctuation theorem that differs noticeably and measurably from it. In particular, for large fluctuations, the ratio of the probability for absorption of heat (by the particle from the fluid) to the probability to supply heat (by the particle to the fluid) is much larger here than in the conventional fluctuation theorem.Comment: 23 pages, 6 figures. Figures are now in color, Eq. (67) was corrected and a footnote was added on the d-dimensional cas

Self-gravitating astrophysical mass with singular central density vibrating in fundamental mode

The fluid-dynamical model of a self-gravitating mass of viscous liquid with singular density at the center vibrating in fundamental mode is considered in juxtaposition with that for Kelvin fundamental mode in a homogeneous heavy mass of incompressible inviscid liquid. Particular attention is given to the difference between spectral formulae for the frequency and lifetime of $f$-mode in the singular and homogeneous models. The newly obtained results are discussed in the context of theoretical asteroseismology of pre-white dwarf stage of red giants and stellar cocoons -- spherical gas-dust clouds with dense star-forming core at the center.Comment: Mod. Phys. Lett. A, Vol. 24, No. 40 (2009) pp. 3257-327

A Wind Driven Warping Instability in Accretion Disks

A wind passing over a surface may cause an instability in the surface such as the flapping seen when wind blows across a flag or waves when wind blows across water. We show that when a radially outflowing wind blows across a dense thin rotating disk, an initially flat disk is unstable to warping. When the wind is subsonic, the growth rate is dependent on the lift generated by the wind and the phase lag between the pressure perturbation and the vertical displacement in the disk caused by drag. When the wind is supersonic, the grow rate is primarily dependent on the form drag caused by the surface. While the radiative warping instability proposed by Pringle is promising for generating warps near luminous accreting objects, we expect the wind driven instability introduced here would dominate in objects which generate energetic outflows

Testing and selection of cosmological models with (1+z)6(1+z)^6 corrections

In the paper we check whether the contribution of $(-)(1+z)^6$ type in the Friedmann equation can be tested. We consider some astronomical tests to constrain the density parameters in such models. We describe different interpretations of such an additional term: geometric effects of Loop Quantum Cosmology, effects of braneworld cosmological models, non-standard cosmological models in metric-affine gravity, and models with spinning fluid. Kinematical (or geometrical) tests based on null geodesics are insufficient to separate individual matter components when they behave like perfect fluid and scale in the same way. Still, it is possible to measure their overall effect. We use recent measurements of the coordinate distances from the Fanaroff-Riley type IIb (FRIIb) radio galaxy (RG) data, supernovae type Ia (SNIa) data, baryon oscillation peak and cosmic microwave background radiation (CMBR) observations to obtain stronger bounds for the contribution of the type considered. We demonstrate that, while $\rho^2$ corrections are very small, they can be tested by astronomical observations -- at least in principle. Bayesian criteria of model selection (the Bayesian factor, AIC, and BIC) are used to check if additional parameters are detectable in the present epoch. As it turns out, the $\Lambda$CDM model is favoured over the bouncing model driven by loop quantum effects. Or, in other words, the bounds obtained from cosmography are very weak, and from the point of view of the present data this model is indistinguishable from the $\Lambda$CDM one.Comment: 19 pages, 1 figure. Version 2 generally revised and accepted for publicatio

Information criteria for efficient quantum state estimation

Recently several more efficient versions of quantum state tomography have been proposed, with the purpose of making tomography feasible even for many-qubit states. The number of state parameters to be estimated is reduced by tentatively introducing certain simplifying assumptions on the form of the quantum state, and subsequently using the data to rigorously verify these assumptions. The simplifying assumptions considered so far were (i) the state can be well approximated to be of low rank, or (ii) the state can be well approximated as a matrix product state. We add one more method in that same spirit: we allow in principle any model for the state, using any (small) number of parameters (which can, e.g., be chosen to have a clear physical meaning), and the data are used to verify the model. The proof that this method is valid cannot be as strict as in above-mentioned cases, but is based on well-established statistical methods that go under the name of "information criteria." We exploit here, in particular, the Akaike Information Criterion (AIC). We illustrate the method by simulating experiments on (noisy) Dicke states