Maxwell’s demon and the second law of thermodynamics

An idealized, two-dimensional Maxwell demon is described which incorporates an irreversible process. The vertex of the device acts as a purely mechanical ‘trap door’. This idealized mechanism is found to generate a violation of the second law of thermodynamics. These results indicate that the second law of thermodynamics is not valid in general for idealized, irreversible systems.     

Dissipative Collapse in the Presence of Λ

We present the general junction conditions for the smooth matching of a spherically symmetric, shear-free spacetime to Vaidya’s outgoing metric across a four-dimensional time-like hypersurface in the presence of a cosmological constant. These results generalise earlier treatments by Santos and co-workers on radiating stellar models. We study the thermal evolution of a particular radiating model within the framework of extended irreversible thermodynamics.     

On the Validity of Entropy Production Principles for Linear Electrical Circuits

We explain the (non-)validity of close-to-equilibrium entropy production principles in the context of linear electrical circuits. Both the minimum and the maximum entropy production principles are understood within dynamical fluctuation theory. The starting point are Langevin equations obtained by combining Kirchoff’s laws with a Johnson-Nyquist noise at each dissipative element in the circuit. The main observation is that the fluctuation functional for time averages, that can be read off from the path-space action, is in first order around equilibrium given by an entropy production rate. That allows to understand beyond the schemes of irreversible thermodynamics (1) the validity of the least dissipation, the minimum entropy production, and the maximum entropy production principles close to equilibrium; (2) the role of the observables’ parity under time-reversal and, in particular, the origin of Landauer’s counterexample (1975) from the fact that the fluctuating observable there is odd under time-reversal; (3) the critical remark of Jaynes (1980) concerning the apparent inappropriateness of entropy production principles in temperature-inhomogeneous circuits.     

Fluid mechanics revisited

Öttinger's recent nontraditional incorporation of fluctuations into the formulation of the friction matrix appearing in the phenomenological GENERIC theory of nonequilibrium irreversible processes is shown to furnish transport equations for single-component gases and liquids undergoing heat transfer which support the view that revisions to the Navier–Stokes–Fourier (N–S–F) momentum/energy equation set are necessary, as empirically proposed by the author on the basis of an experimentally supported theory of diffuse volume transport. The hypothesis that the conventional N–S–F equations prevail without modification only in the case of “incompressible” fluids, where the density ρ of the fluid is uniform throughout, serves to determine the new phenomenological parameter α^′ appearing in the GENERIC friction matrix. In the case of ideal gases the consequences of this constitutive hypothesis are shown to yield results identical to those derived theoretically by Öttinger on the basis of a “proper” coarse-graining of Boltzmann's kinetic equation. A major consequence of the present work is that the fluid's specific momentum density v is equal to its volume velocity v_v, rather than to its mass velocity v_m, contrary to current views dating back 250 years to Euler. In the case of rarefied gases the proposed modifications are also observed to agree with those resulting from Klimontovich's molecularly based, albeit ad hoc, self-diffusion addendum to Boltzmann's collision integral. Despite the differences in their respective physical models—molecular vs. phenomenological—the role played by Klimontovich's collisional addition to Boltzmann's equation in modifying the N–S–F equations is noted to constitute a molecular counterpart of Öttinger's phenomenological fluctuation addition to the GENERIC friction matrix. Together, these two theories collectively recognize the need to address multiple- rather than single-encounter collisions between a test molecule and its neighbors when formulating physically satisfactory statistical–mechanical theories of irreversible transport processes in gases. Overall, the results of the present work implicitly support the unorthodox view, implicit in the GENERIC scheme, that the translation of Newton's discrete mass-point molecular mechanics into continuum mechanics, the latter as embodied in the Cauchy linear momentum equation of fluid mechanics, cannot be correctly effected independently of the laws of thermodynamics. While Öttinger's modification of GENERIC necessitates fundamental changes in the foundations of fluid mechanics in regard to momentum transport, no basic changes are required in the foundations of linear irreversible thermodynamics (LIT) beyond recognizing the need to add volume to the usual list of extensive physical properties undergoing transport in single-species fluid continua, namely mass, momentum and energy. An alternative, nonGENERICally based approach to LIT, derived from our findings, is outlined at the conclusion of the paper. Finally, our proposed modifications of both Cauchy's linear momentum equation and Newton's rheological constitutive law for fluid-phase continua are noted to be mirrored by counterparts in the literature for solid-phase continua dating back to the classical interdiffusion experiments of Kirkendall and their subsequent interpretation by Darken in terms of diffuse volume transport.     

Stability and causality in dissipative relativistic fluids

The standard theory of relativistic dissipative fluid mechanics developed by Eckart contains several undesirable features: thermal and viscous fluctuations propagate acausally; there exist generic short wavelength secular instabilities; and there is not a well posed initial value problem for rotating fluids. In this paper we examine whether the generalization of Eckart's theory developed by Israel has succeeded in eliminating these features. We first generalize Israel's theory to include the possibility of nonuniform equilibrium configurations. This generalization allows us to describe equilibrium configurations which may be rotating and self-gravitating such as neutron stars. We then evaluate the stability conditions for these fluids and compute the characteristic velocities at which perturbations propagate. Our main result is that if these fluids are stable, then the characteristic velocities are subluminal and the perturbations propagate via hyperbolic equations. Thus Israel's theory is causal for all stable fluids. In addition, there is no generic instability, and the initial value problem is well posed. In our opinion, for these reasons, Israel's theory should replace Eckart's as the standard theory of relativistic dissipative fluid mechanics.     

Arc root dynamics in high power plasma torches — Evidence of chaotic behavior

Although plasma torches have been commercially available for about 50 years, areas such as plasma gun design, process efficiency, reproducibility, plasma stability, torch lives etc. have remained mostly unattended. Recent torch developments have been focusing on the basic understanding of the plasma column and its dynamics inside the plasma torch, the interaction of plasma jet and the powders, the interaction of the plasma jet with surroundings and the impingement of the jet on the substrate. Two of the major causes of erratic and poor performance of a variety of thermal plasma processes are currently identified as the fluctuations arising out of the arc root movement on the electrodes inside the plasma torch and the fluid dynamic instabilities arising out of entrainment of the air into the plasma jet. This paper reviews the current state of understanding of these fluctuations as well as the dynamics of arc root movement in plasma torches. The work done at the author’s laboratory on studying the fluctuations in arc voltage, arc current, acoustic emissions and optical emissions are also presented. These fluctuations are observed to be chaotic and interrelated. Real time monitoring and controlling the arc instabilities through chaos characterization parameters can greatly contribute to the understanding of electrode erosion as well as improvement of plasma torch lifetime.     

Contact symmetries and Hamiltonian thermodynamics

It has been shown that contact geometry is the proper framework underlying classical thermodynamics and that thermodynamic fluctuations are captured by an additional metric structure related to Fisher’s Information Matrix. In this work we analyse several unaddressed aspects about the application of contact and metric geometry to thermodynamics. We consider here the Thermodynamic Phase Space and start by investigating the role of gauge transformations and Legendre symmetries for metric contact manifolds and their significance in thermodynamics. Then we present a novel mathematical characterization of first order phase transitions as equilibrium processes on the Thermodynamic Phase Space for which the Legendre symmetry is broken. Moreover, we use contact Hamiltonian dynamics to represent thermodynamic processes in a way that resembles the classical Hamiltonian formulation of conservative mechanics and we show that the relevant Hamiltonian coincides with the irreversible entropy production along thermodynamic processes. Therefore, we use such property to give a geometric definition of thermodynamically admissible fluctuations according to the Second Law of thermodynamics. Finally, we show that the length of a curve describing a thermodynamic process measures its entropy production.     

Relativistic Dynamics of Accelerating Particles Derived from Field Equations

In relativistic mechanics the energy-momentum of a free point mass moving without acceleration forms a four-vector. Einstein’s celebrated energy-mass relation E=mc ² is commonly derived from that fact. By contrast, in Newtonian mechanics the mass is introduced for an accelerated motion as a measure of inertia. In this paper we rigorously derive the relativistic point mechanics and Einstein’s energy-mass relation using our recently introduced neoclassical field theory where a charge is not a point but a distribution. We show that both the approaches to the definition of mass are complementary within the framework of our field theory. This theory also predicts a small difference between the electron rest mass relevant to the Penning trap experiments and its mass relevant to spectroscopic measurements.     

Relativistic generalization of Bell’s inequalities in Wigner’s form

A relativistic generalization of Bell’s inequalities in Wigner’s form was obtained for the decays of a pseudoscalar and a scalar particle to two particles having a nonzero spin (fermions and photons). Both inequalities involving a full anticorrelation of final-particle spins and having a nonrelativistic analog and inequalities involving a full correlation of spins are considered. It is shown that Bohr’s complementarity principle may be tested experimentally in the relativistic region.     

Relativistic perihelion precession of orbits of Venus and the Earth

Among all the theories proposed to explain the “anomalous” perihelion precession of Mercury’s orbit first announced in 1859 by Le Verrier, the general theory of relativity proposed by Einstein in November 1915 alone could calculate Mercury’s “anomalous” precession with the precision demanded by observational accuracy. Since Mercury’s precession was a directly derived result of the full general theory, it was viewed by Einstein as the most critical test of general relativity from amongst the three tests he proposed. With the advent of the space age, the level of observational accuracy has improved further and it is now possible to detect this precession for other planetary orbits of the solar system — viz., Venus and the Earth. This conclusively proved that the phenomenon of “anomalous” perihelion precession of planetary orbits is a relativistic effect. Our previous papers presented the mathematical model and the computed value of the relativistic perihelion precession of Mercury’s orbit using an alternate relativistic gravitational model, which is a remodeled form of Einstein’s relativity theories, and which retained only experimentally proven principles. In addition this model has the benefit of data from almost a century of relativity experimentation, including those that have become possible with the advent of the space age. Using this model, we present in this paper the computed values of the relativistic precession of Venus and the Earth, which compare well with the predictions of general relativity and are also in agreement with the observed values within the range of uncertainty.      

Global Solutions to the Ultra-Relativistic Euler Equations

We show that when entropy variations are included and special relativity is imposed, the thermodynamics of a perfect fluid leads to two distinct families of equations of state whose relativistic compressible Euler equations are of Nishida type. (In the non-relativistic case there is only one.) The first corresponds exactly to the Stefan-Boltzmann radiation law, and the other, emerges most naturally in the ultra-relativistic limit of a γ-law gas, the limit in which the temperature is very high or the rest mass very small. We clarify how these two relativistic equations of state emerge physically, and provide a unified analysis of entropy variations to prove global existence in one space dimension for the two distinct 3 × 3 relativistic Nishida-type systems. In particular, as far as we know, this provides the first large data global existence result for a relativistic perfect fluid constrained by the Stefan-Boltzmann radiation law.     

Einstein,de Sitter and the beginning of relativistic cosmology in 1917

In 1917, both Einstein and de Sitter proposed a new interpretation of the universe as a whole: the structure of the universe could be described in terms of relativistic field equations. Their contributions marked the beginning of the modern scientific comprehension of the origin and evolution of the universe. Our aim is to propose a critical review paper, based on references in primary sources, on the formulation in 1917 of Einstein’s and de Sitter’s models of the universe, which represents a fundamental chapter in the history of relativistic Cosmology.     

Acoustic scattering by turbulent fluctuations of pressure and entropy

Detailed analysis is presented of the well-known Tatarskii’s formula, which describes sound wave scattering in a turbulent atmosphere. The adiabaticity of the acoustic fluctuations and incompressibility of the turbulent fluctuations are assumed only. This yields to additional 1 terms in the classical formula (probably, small in the inertial range of turbulence). We show the change of Obukhov’s formula, which describes the connection between turbulent fluctuations of pressure and velocities in a compressible atmosphere, and also demonstrate the effect of the independence of fluctuations of the potential and thermodynamic temperatures. By analogy with the formula for small-scale isotropic temperature fluctuations, which was also obtained by Obukhov, we derive a formula for the fluctuations of entropy and potential density as function of entropy, which describes spatial distribution of the probability density of identical “fluid particles” in the turbulent media.     

The effect of hydrodynamical instabilities and of convection in the conversion of an hadronic star to a more compact object

We study the hydrodynamical transition from an hadronic star into a quark or a hybrid star. We discuss the possible mode of burning, using a fully relativistic formalism and realistic Equations of State in which hyperons can be present. We take into account the possibility that quarks form a diquark condensate. We find that the conversion process always corresponds to a deflagration and never to a detonation. Hydrodynamical instabilities can develop on the front but the increase in the conversion’s velocity is not sufficient to transform the deflagration into a detonation. Concerning convection, it does not always develop. Instead, the process of conversion from ungapped quark matter to gapped quarks always allows the formation of a convective layer. The text was submitted by the authors in English.     

On the thermodynamics of phase transitions in metal hydrides

Metal hydrides are solutions of hydrogen in a metal, where phase transitions may occur depending on temperature, pressure etc. We apply Le Chatelier’s principle of thermodynamics to a particular phase transition in TiH _x , which can approximately be described as a second-order phase transition. We show that the fluctuations of the order parameter correspond to fluctuations both of the density of H⁺ ions and of the distance between adjacent H⁺ ions. Moreover, as the system approaches the transition and the correlation radius increases, we show -with the help of statistical mechanics-that the statistical weight of modes involving a large number of H⁺ ions (‘collective modes’) increases sharply, in spite of the fact that the Boltzmann factor of each collective mode is exponentially small. As a result, the interaction of the H⁺ ions with collective modes makes a tiny suprathermal fraction of the H⁺ population appear. Our results hold for similar transitions in metal deuterides, too. A violation of an -insofar undisputed-upper bound on hydrogen loading follows.     

Poincaré’s Relativistic Physics: Its Origins and Nature

Henri Poincaré (1854–1912) developed a relativistic physics by elevating the empirical inability to detect absolute motion, or motion relative to the ether, to the principle of relativity, and its mathematics ensured that it would be compatible with that principle. Although Poincaré’s aim and theory were similar to those of Albert Einstein (1879–1955) in creating his special theory of relativity, Poincaré’s relativistic physics should not be seen as an attempt to achieve Einstein’s theory but as an independent endeavor. Poincaré was led to advance the principle of relativity as a consequence of his reflections on late nineteenth-century electrodynamics; of his conviction that physics should be formulated as a physics of principles; of his conventionalistic arguments on the nature of time and its measurement; and of his knowledge of the experimental failure to detect absolute motion. The nonrelativistic theory of electrodynamics of Hendrik A.Lorentz (1853–1928) of 1904 provided the means for Poincaré to elaborate a relativistic physics that embraced all known physical forces, including that of gravitation. Poincaré did not assume any dynamical explanation of the Lorentz transformation, which followed from the principle of relativity, and he did not seek to dismiss classical concepts, such as that of the ether, in his new relativistic physics. Shaul Katzir teaches in the Graduate Program in History and Philosophy of Science, Bar Ilan University.     

Cutting DNA: Mechanics of the topoisomerase

The framework of relativistic self-consistent mean-field models is extended to include correlations related to restoration of broken symmetries and to fluctuations of collective variables. The generator coordinate method is used to perform configuration mixing of angular-momentum and particle-number projected relativistic wave functions. The model, currently restricted to axially symmetric shapes, employs a relativistic point-coupling (contact) nucleon-nucleon effective interaction in the particle-hole channel, and a δ-interaction in the pairing channel. Both bulk and spectroscopic nuclear properties are explored.