Maxwell’s demon and the management of ignorance in stochastic thermodynamics

It is nearly 150 years since Maxwell challenged the validity of the second law of thermodynamics by imagining a tiny creature who could sort the molecules of a gas in such a way that would decrease entropy without exerting any work. The demon has been discussed largely using thought experiments, but it has recently become possible to exert control over nanoscale systems, just as Maxwell imagined, and the status of the second law has become a more practical matter, raising the issue of how measurements manage our ignorance in a way that can be exploited. The framework of stochastic thermodynamics extends macroscopic concepts such as heat, work, entropy and irreversibility to small systems and allows us explore the matter. Some arguments against a successful demon imply a second law that can be suspended indefinitely until we dissipate energy in order to remove the records of his operations. In contrast, under stochastic thermodynamics, the demon fails because on average, more work is performed upfront in making a measurement than can be extracted by exploiting the outcome. This requires us to exclude systems and a demon that evolve under what might be termed self-sorting dynamics, and we reflect on the constraints on control that this implies while still working within a thermodynamic framework.     

Penrose’s circles in the CMB and a test of inflation

We present a calculation of the angular size of the circles in the CMB predicted by Penrose on the basis of his conformal cyclic cosmology. If these circles are detected, the existence of an upper limit on their angular radius would provide a challenge for inflation.     

Republication of: On the formal analogy between the basic electromagnetic equations and Einstein’s gravity equations in first approximation

This is an English translation of a paper by Hans Thirring, first published in German in 1918, which contains the first and correct presentation of the basic equations of gravitomagnetism in linear order. The paper has been selected by the Editors of General Relativity and Gravitation for republication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by Herbert Pfister, and Thirring’s brief biography compiled by Andrzej Krasinski from internet sources     

Existence and Asymptotic Stability of Periodic Solutions of the Reaction–Diffusion Equations in the Case of a Rapid Reaction

A singularly perturbed periodic in time problem for a parabolic reaction-diffusion equation in a two-dimensional domain is studied. The case of existence of an internal transition layer under the conditions of balanced and unbalanced rapid reaction is considered. An asymptotic expansion of a solution is constructed. To justify the asymptotic expansion thus constructed, the asymptotic method of differential inequalities is used. The Lyapunov asymptotic stability of a periodic solution is investigated.     

Cosmic rays and variations of the concentration of active nuclei of condensation and crystallization in the Earth’s atmosphere

A possible mechanism of the influence of cosmic rays on the concentration of neutral active nuclei of condensation and crystallization in the Earth’s atmosphere is considered. The mechanism is based on the variation in the transparency of the atmosphere under cosmic rays. It is shown that the concentration of active nuclei of condensation increase at low and middle altitudes, while the concentration of stable ice nuclei decreases. This effect and the change in the growth rate of drops can lead to correlation between the galactic cosmic rays and cloud cover anomalies at low altitudes and to the absence of correlation at middle altitudes. It is shown that the correlation between galactic cosmic rays and cloud cover anomalies can be absent at high altitudes.     

Comparative study on electroosmosis modulated flow of MHD viscoelastic fluid in the presence of modified Darcy’s law

Magnetic field plays an important role in numerous fields such as biological, chemical, mechanical and medical research. In clinical and medical research the high field magnets are extremely important to create 3D images of anatomical and diagnostic importance from nuclear magnetic resonance signals. In view of these applications, the purpose of present work is to explore the impact of an external magnetic field on the viscoelastic fluid flow in the existence of electroosmosis, porous medium and slip boundary conditions. The governing equation is modified under the suitable dimensionless quantities. The resulting non-dimensional differential equation is evaluated by analytical as well as numerical (finite difference and cubic B-spline) methods. The convergence analysis is also presented for the numerical methods. The variations of sundry parameters on velocity, volume flow rate and skin friction are presented through graphical representations. The current analysis depicts that, the higher velocities are noticed in viscoelastic fluid as compared with Newtonian fluid. The velocity enhances with rising of slip and Darcy parameters. Volume flow rate rises with the slip and viscoelastic parameters. Skin friction is a decreasing function of zeta potential, Darcy number and Hall current parameter. The limiting solutions can be captured for the Newtonian fluid model by setting the viscoelastic parameter to zero.     

On Ohm’s law in the thin current sheets of the Earth’s magnetosphere

The analytical and numerical dependences of the total transverse current on an electric field, the normal component of a magnetic field and the ion and electron temperatures are obtained using analytical approximation of numerical results provided by a self-consistent model of the magnetospheric thin sheet. The dependence of current on the parameters ?, T _i , b _n is shown to be nonlinear. The relative contributions of different plasma components into the total current are estimated.     

Landauer’s limit and the physicality of information

Landauer’s lower bound on the dissipative cost of information erasure is revisited within a new physical conception of information. The notion of strong physical information is introduced, and the new conception of physical information – observer-local referential (OLR) information – is defined, shown to be strongly physical, and related to other measures that arise in physical information contexts. A generalization of Landauer’s limit is then obtained for OLR information from quantum dynamics and entropic inequalities alone. Specializations of this bound are compared and contrasted to similar bounds under conditions for which they coincide, and important distinctions between seemingly identical bounds expressed in terms of various information measures are discussed. The controversial distinction between Landauer erasure of known and unknown data – and the alleged difference between their respective erasure costs – is then explored via OLR information. This physically grounds and clarifies distinctions between known and unknown data and between unconditional and conditional erasure operations, enables a straightforward physical accounting of associated lower bounds on erasure costs, and illustrates the advantages of OLR information for resolution of controversies related to the dissipative cost of information erasure. Applications of OLR information to determination of irreversibility induced dissipation bounds in more complex computing scenarios are briefly discussed.     

Gradual learning and the evolution of cooperation in the spatial Continuous Prisoner’s Dilemma

The usual mechanism for modeling learning in spatially structured evolutionary games has to date been imitation of some successful neighbor. However, it seems natural that individuals hesitate to imitate their neighbor’s acts, specially if they can imply high costs. Here we study the effect of incorporating resistance to imitation on these models. Our framework is the spatial Continuous Prisoner’s Dilemma. For this evolutionary game, it has been reported that occasional errors in the imitation process can explain the emergence of cooperation from a non-cooperative initial state. In this work, we show that this only occurs for particular regimes of low costs of cooperation. Furthermore, we display how resistance gets greater the range of scenarios where cooperative individuals can invade selfish populations. In this context, where resistance to imitation can be interpreted as a general rule of gradual learning, our results show that the less that is learnt in a single step from a successful neighbors, the larger the degree of global cooperation finally attained. In general, the effect of step-by-step learning can be more efficient for the evolution of cooperation than a full blast one.     

Young’s modulus and the Poisson’s ratio of planar and nanotubular supracrystalline structures

A method has been proposed for calculating the two-dimensional Young??s modulus and the Poisson??s ratio for planar and nanotubular structures through the components of the two-dimensional elastic rigidity tensor obtained by numerical methods. The method has been tested for graphene and two-dimensional supracrystalline sheets.     

The relation between Hardy’s non-locality and violation of Bell inequality

We give an analytic quantitative relation between Hardy’s non-locality and Bell operator. We find that Hardy’s non-locality is a sufficient condition for the violation of Bell inequality, the upper bound of Hardy’s non-locality allowed by information causality just corresponds to Tsirelson bound of Bell inequality and the upper bound of Hardy’s non-locality allowed by the principle of no-signaling just corresponds to the algebraic maximum of Bell operator. Then we study the Cabello’s argument of Hardy’s non-locality (a generalization of Hardy’s argument) and find a similar relation between it and violation of Bell inequality. Finally, we give a simple derivation of the bound of Hardy’s non-locality under the constraint of information causality with the aid of the above derived relation between Hardy’s non-locality and Bell operator.     

Is the Kramers-Kronig relationship between ultrasonic attenuation and dispersion maintained in the presence of apparent losses due to phase cancellation?

Phase cancellation effects can compromise the integrity of ultrasonic measurements performed with phase sensitive receiving apertures. A lack of spatial coherence of the ultrasonic field incident on a phase sensitive receiving array can produce inaccuracies of the measured attenuation coefficient and phase velocity. The causal (Kramers-Kronig) link between these two quantities in the presence of phase distortion is investigated using two plastic polymer materials, Plexiglas and Lexan, that exhibit attenuation coefficients that increase linearly with frequency, in a fashion analogous to that of soft tissue. Flat and parallel plates were machined to have a step of a thickness corresponding to an integer number of half wavelengths within the bandwidth investigated, 3 to 7 MHz. Insonification of the stepped portion of each plate produces phase cancellation artifacts at the receiving aperture and, therefore, in the measured frequency dependent attenuation coefficient. Dispersion predictions using two different forms of the Kramers-Kronig relations were performed for the flat and the stepped regions of each plastic plate. Despite significant phase distortion and a detection system sensitive to these aberrations, the Kramers-Kronig link between the apparent attenuation coefficient and apparent phase velocity dispersion remains intact.     

Dependence of the lidar signal depolarization on the receiver’s field of view in the sounding of fog and clouds

We report an experimental study of the lidar signal depolarization as a function of the relative contribution of the multiple scattering in case of optically dense objects in the atmospheric planetary boundary layer. Results of the observation of fog and stratus clouds are presented, as well as those obtained by sounding of stratocumulus clouds during a snowfall. The lidar data point to a rise of the depolarization coefficient as the influence of the multiple scattering increases in consequence of both viewing angle enlargement and penetration into the object sounded. The variations of the depolarization coefficient are studied as a function of the field of view. In the case of fog, this dependence is approximated by a three-parameter exponential law; it is found that the depolarization increases steeply when the viewing angle is increased from 9 mrad to 12.5 mrad. The relationships between the approximation parameters and the microphysical characteristics of the scattering medium are considered. The experimentally determined size of the area where multiple scattering occurs is in good agreement with that calculated according to the diffusion model. The results obtained on the multiple scattering effect on the depolarization can also be employed in determining the extinction coefficient profiles in optically dense objects, as well as in evaluating the characteristic size of the scattering particles. Received: 6 September 1999 / Revised version: 7 February 2000 / Published online: 6 September 2000     

Classification of vibrational resonances in the energy spectrum of the formaldehyde molecule and Katz’s branch points

The Rayleigh–Schrödinger perturbation theory of high orders and the algebraic Padé–Hermite approximants are used to determine the singular points of a vibrational energy function of the formaldehyde molecule dependent on a complex perturbation parameter as on the argument. It is shown that the Fermi, Darling–Dennison, and other higher-order vibrational resonances are related to Katz’s points—common branch points on the complex plane of the energy of two vibrational states. Analysis of Katz’s points that connect different vibrational states allows one to reveal essential resonance perturbations, to introduce an additional classification for them, and to determine the polyad structure of an energy spectrum.     

Density inhomogeneities of the Earth’s mantle and core

Lateral density variations are determined at depth and are characterized by the anomalies of the seismic waves velocities, which are consistent with both the anomalies of the external gravity field and with the data from the analysis of Earth’s free-oscillation minimizing the deviations of the internal Earth structure from a hydrostatically equilibrated structure. It is shown that the obtained anomalous structures cause anomalies of the gravity field inside the Earth, which may be conducive to convective movements in the mantle and core.     

A study of non-extensivity in the Earth’s magnetosphere

Magnetic storms are undoubtedly among the most important phenomena in space physics and also a central subject of space weather. The non-extensive Tsallis entropy has been recently introduced, as an effective complexity measure for the analysis of the geomagnetic activity D _st index. Tsallis entropy has been shown to sensitively detect the complexity dissimilarity between pre-storm activity and intense magnetic storms in the Earth’s magnetosphere. Here, we show that the D _st time series obey a modified form of the Gutenberg-Richter law for the case of non-extensive statistics, thus providing evidence for universality in magnetic storm and earthquake occurrence.     

Degree and connectivity of the Internet’s scale-free topology

This paper theoretically and empirically studies the degree and connectivity of the Internet's scale-free topology at an autonomous system (AS) level. The basic features of scale-free networks influence the normalization constant of degree distribution p(k). It develops a new mathematic model for describing the power-law relationships of Internet topology. From this model we theoretically obtain formulas to calculate the average degree, the ratios of the k_min-degree (minimum degree) nodes and the k_max-degree (maximum degree) nodes, and the fraction of the degrees (or links) in the hands of the richer (top best-connected) nodes. It finds that the average degree is larger for a smaller power-law exponent λ and a larger minimum or maximum degree. The ratio of the k_min-degree nodes is larger for larger λ and smaller k_min or k_max. The ratio of the k_max-degree ones is larger for smaller λ and k_max or larger k_min. The richer nodes hold most of the total degrees of Internet AS-level topology. In addition, it is revealed that the increased rate of the average degree or the ratio of the k_min-degree nodes has power-law decay with the increase of k_min. The ratio of the k_max-degree nodes has a power-law decay with the increase of k_max, and the fraction of the degrees in the hands of the richer 27% nodes is about 73% (the '73/27 rule'). Finally, empirically calculations are made, based on the empirical data extracted from the Border Gateway Protocol, of the average degree, ratio and fraction using this method and other methods, and find that this method is rigorous and effective for Internet AS-level topology.