A heat pump at a molecular scale controlled by a mechanical force

We show that a mesoscopic system such as Feynman's ratchet may operate as a heat pump, and clarify a underlying physical picture. We consider a system of a particle moving along an asymmetric periodic structure . When put into a contact with two distinct heat baths of equal temperature, the system transfers heat between two baths as the particle is dragged. We examine Onsager relation for the heat flow and the particle flow, and show that the reciprocity coefficient is a product of the characteristic heat and the diffusion constant of the particle. The characteristic heat is the heat transfer between the baths associated with a barrier-overcoming process. Because of the correlation between the heat flow and the particle flow, the system can work as a heat pump when the particle is dragged. This pump is particularly effective at molecular scales where the energy barrier is of the order of the thermal energy.Comment: 7 pages, 5 figures; revise

Scale-dependent bias of galaxies and mu-type distortion of the cosmic microwave background spectrum from single-field inflation with a modified initial state

We investigate the phenomenological consequences of a modification of the initial state of a single inflationary field. While single-field inflation with the standard Bunch-Davies initial vacuum state does not generally produce a measurable three-point function (bispectrum) in the squeezed configuration, allowing for a non-standard initial state produces an exception. Here, we calculate the signature of an initial state modification in single-field slow-roll inflation in both the scale-dependent bias of the large-scale structure (LSS) and mu-type distortion in the black-body spectrum of the cosmic microwave background (CMB). We parametrize the initial state modifications and identify certain choices of parameters as natural, though we also note some fine-tuned choices that can yield a larger bispectrum. In both cases, we observe a distinctive k^-3 signature in LSS (as opposed to k^-2 for the local-form). As a non-zero bispectrum in the squeezed configuration correlates a long-wavelength mode with two short-wavelength modes, it induces a correlation between the CMB temperature anisotropy on large scales with the temperature-anisotropy-squared on very small scales; this correlation persists as the small-scale anisotropy-squared is processed into mu-type distortions. While the local-form mu-distortion turns out to be too small to detect in the near future, a modified initial vacuum state enhances the signal by a large factor owing to an extra factor of k_1/k. For example, a proposed absolutely-calibrated experiment, PIXIE, is expected to detect this correlation with a signal-to-noise ratio greater than 10, for an occupation number of about 0.5 in the observable modes. Relatively calibrated experiments such as Planck and LiteBIRD should also be able to measure this effect, provided that the relative calibration between different frequencies meets the required precision. (Abridged)Comment: 14 pages, 6 figures. Matches version in PRD. Improved explanation in Sec. IV; added references and corrected typo

Relativistic stars with purely toroidal magnetic fields

We investigate the effects of the purely toroidal magnetic field on the equilibrium structures of the relativistic stars. The master equations for obtaining equilibrium solutions of relativistic rotating stars containing purely toroidal magnetic fields are derived for the first time. To solve these master equations numerically, we extend the Cook-Shapiro-Teukolsky scheme for calculating relativistic rotating stars containing no magnetic field to incorporate the effects of the purely toroidal magnetic fields. By using the numerical scheme, we then calculate a large number of the equilibrium configurations for a particular distribution of the magnetic field in order to explore the equilibrium properties. We also construct the equilibrium sequences of the constant baryon mass and/or the constant magnetic flux, which model the evolution of an isolated neutron star as it loses angular momentum via the gravitational waves. Important properties of the equilibrium configurations of the magnetized stars obtained in this study are summarized as follows ; (1) For the non-rotating stars, the matter distribution of the stars is prolately distorted due to the toroidal magnetic fields. (2) For the rapidly rotating stars, the shape of the stellar surface becomes oblate because of the centrifugal force. But, the matter distribution deep inside the star is sufficiently prolate for the mean matter distribution of the star to be prolate. (3) The stronger toroidal magnetic fields lead to the mass-shedding of the stars at the lower angular velocity. (4) For some equilibrium sequences of the constant baryon mass and magnetic flux, the stars can spin up as they lose angular momentum.Comment: 13 figures, 7 tables, submitted to PR

Hidden heat transfer in equilibrium states implies directed motion in nonequilibrium states

We study a class of heat engines including Feynman's ratchet, which exhibits a directed motion of a particle in nonequilibrium steady states maintained by two heat baths. We measure heat transfer from each heat bath separately, and average them using a careful procedure that reveals the nature of the heat transfer associated with directed steps of the particle. Remarkably we find that steps are associated with nonvanishing heat transfer even in equilibrium, and there is a quantitative relation between this ``hidden heat transfer'' and the directed motion of the particle. This relation is clearly understood in terms of the ``principle of heat transfer enhancement'', which is expected to apply to a large class of highly nonequilibrium systems.Comment: 4 pages, 4 figures; revise

Kink Solution in a Fluid Model of Traffic Flows

Traffic jam in a fluid model of traffic flows proposed by Kerner and Konh\"auser (B. S. Kerner and P. Konh\"auser, Phys. Rev. E 52 (1995), 5574.) is analyzed. An analytic scaling solution is presented near the critical point of the hetero-clinic bifurcation. The validity of the solution has been confirmed from the comparison with the simulation of the model.Comment: RevTeX v3.1, 6 pages, and 2 figure

Non-axisymmetric oscillations of rapidly rotating relativistic stars by conformal flatness approximation

We present a new numerical code to compute non-axisymmetric eigenmodes of rapidly rotating relativistic stars by adopting spatially conformally flat approximation of general relativity. The approximation suppresses the radiative degree of freedom of relativistic gravity and the field equations are cast into a set of elliptic equations. The code is tested against the low-order f- and p-modes of slowly rotating stars for which a good agreement is observed in frequencies computed by our new code and those computed by the full theory. Entire sequences of the low order counter-rotating f-modes are computed, which are susceptible to an instability driven by gravitational radiation.Comment: 3 figures. To appear in Phys.Rev.

Leaf area index and topographical effects on turburlent diffusion in a deciduous forest

In order to investigate turbulent diffusion in a deciduous forest canopy, wind velocity measurements were conducted from late autumn of 2009 to early spring of 2010, using an observation tower 20 m in height located in the campus of Kanazawa University. Four sonic anemometers mounted on the tower recorded the average wind velocities and temperatures, as well as their fluctuations, at four different heights simultaneously. Two different types of data sets were selected, in which the wind velocities, wind bearings and atmospheric stabilities were all similar, but the Leaf Area Indexes (LAI's) were different. Vertical profiles of average wind velocities were found to have an approximately exponential profile in each case. The characteristic length scales of turbulence were evaluated by both von Karman's method and the integral time scale deduced from the autocorrelation from time-series analyses. Both methods produced comparable values of eddy diffusivity for the cases with some foliage during late autumn, but some discrepancy in the upper canopy layer was observed when the trees did not have their leaves in early spring. It was also found that the eddy diffusivities generally take greater values at higher positions, where the wind speeds are large. Anisotropy of eddy diffusivities between the vertical and horizontal components was also observed, particularly in the cases when the canopy does not have leaves, when the horizontal eddy diffusivities are generally larger than the vertical ones. On the other hand, the anisotropy is less visible when the trees have some foliage during autumn. The effects of topography on the turbulent diffusion were also investigated, including evaluation of the non-zero time-averaged vertical wind velocities. The results show that the effects are marginal for both cases, and can be neglected as far as diffusion in the canopy is concerned

Entropy and Nonlinear Nonequilibrium Thermodynamic Relation for Heat Conducting Steady States

Among various possible routes to extend entropy and thermodynamics to nonequilibrium steady states (NESS), we take the one which is guided by operational thermodynamics and the Clausius relation. In our previous study, we derived the extended Clausius relation for NESS, where the heat in the original relation is replaced by its "renormalized" counterpart called the excess heat, and the Gibbs-Shannon expression for the entropy by a new symmetrized Gibbs-Shannon-like expression. Here we concentrate on Markov processes describing heat conducting systems, and develop a new method for deriving thermodynamic relations. We first present a new simpler derivation of the extended Clausius relation, and clarify its close relation with the linear response theory. We then derive a new improved extended Clausius relation with a "nonlinear nonequilibrium" contribution which is written as a correlation between work and heat. We argue that the "nonlinear nonequilibrium" contribution is unavoidable, and is determined uniquely once we accept the (very natural) definition of the excess heat. Moreover it turns out that to operationally determine the difference in the nonequilibrium entropy to the second order in the temperature difference, one may only use the previous Clausius relation without a nonlinear term or must use the new relation, depending on the operation (i.e., the path in the parameter space). This peculiar "twist" may be a clue to a better understanding of thermodynamics and statistical mechanics of NESS.Comment: 31 pages, 4 figure

An expression for stationary distribution in nonequilibrium steady state

We study the nonequilibrium steady state realized in a general stochastic system attached to multiple heat baths and/or driven by an external force. Starting from the detailed fluctuation theorem we derive concise and suggestive expressions for the corresponding stationary distribution which are correct up to the second order in thermodynamic forces. The probability of a microstate $\eta$ is proportional to $\exp[{\Phi}(\eta)]$ where ${\Phi}(\eta)=-\sum_k\beta_k\mathcal{E}_k(\eta)$ is the excess entropy change. Here $\mathcal{E}_k(\eta)$ is the difference between two kinds of conditioned path ensemble averages of excess heat transfer from the $k$-th heat bath whose inverse temperature is $\beta_k$. Our expression may be verified experimentally in nonequilibrium states realized, for example, in mesoscopic systems.Comment: 4 pages, 2 figure

Losing Weight: A KECK Spectroscopic Survey of the Massive Cluster of Galaxies RX J1347-1145

We present a sample of 47 spectroscopically confirmed members of RX J1347-1145, the most luminous X-ray cluster of galaxies discovered to date. With two exceptions, all the galaxies in this sample have red B-R colors and red spectral indices, with spectra similar to old local ellipticals. Using all 47 cluster members, we derive a mean redshift of 0.4509\pm 0.003, and a velocity dispersion of 910\pm130 km/sec, which corresponds to a virial mass of 4.4 x 10^{14} h^{-1} Solar masses with an harmonic radius of 380 h^{-1} kpc. The derived total dynamical mass is marginally consistent with that deduced from the cluster's X-ray emission based on the analysis of ROSAT/ASCA images (Schindler et al. 1997), but not consistent with the more recent X-ray analyses of Allen (2000), Ettori, Allen & Fabian (2001) and Allen, Schmidt & Fabian (2002). Furthermore, the dynamical mass is significantly smaller than that derived from weak lensing (Fischer & Tyson 1997) and from strong lensing (Sahu et al. 1998). We propose that these various discrepant mass estimates may be understood if RX J1347-1145 is the product of two clusters caught in the act of merging in a direction perpendicular to the line of sight, although there is no evidence from the galaxy redshift distribution supporting this hypothesis. Even with this hypothesis, a significant part of the extremely high X-ray luminosity must still arise from non-virialized, presumably shocked, gas. Finally, we report the serendipitous discovery of a lensed background galaxy at z=4.083 which will put strong constraints on the lensing mass determination once its counter-image is securely identified.Comment: Minor changes to conform to version accepted by Ap