Relativistic Equilibrium Distribution by Relative Entropy Maximization

The equilibrium state of a relativistic gas has been calculated based on the maximum entropy principle. Though the relativistic equilibrium state was long believed to be the Juttner distribution, a number of papers have been published in recent years proposing alternative equilibrium states. However, some of these papers do not pay enough attention to the covariance of distribution functions, resulting confusion in equilibrium states. Starting from a fully covariant expression to avoid this confusion, it has been shown in the present paper that the Juttner distribution is the maximum entropy state if we assume the Lorentz symmetry.Comment: Six pages, no figure

Stationarity, soft ergodicity, and entropy in relativistic systems

Recent molecular dynamics simulations show that a dilute relativistic gas equilibrates to a Juettner velocity distribution if ensemble velocities are measured simultaneously in the observer frame. The analysis of relativistic Brownian motion processes, on the other hand, implies that stationary one-particle distributions can differ depending on the underlying time-parameterizations. Using molecular dynamics simulations, we demonstrate how this relativistic phenomenon can be understood within a deterministic model system. We show that, depending on the time-parameterization, one can distinguish different types of soft ergodicity on the level of the one-particle distributions. Our analysis further reveals a close connection between time parameters and entropy in special relativity. A combination of different time-parameterizations can potentially be useful in simulations that combine molecular dynamics algorithms with randomized particle creation, annihilation, or decay processes.Comment: 4 page

Thermal equilibrium and statistical thermometers in special relativity

There is an intense debate in the recent literature about the correct generalization of Maxwell's velocity distribution in special relativity. The most frequently discussed candidate distributions include the Juettner function as well as modifications thereof. Here, we report results from fully relativistic one-dimensional (1D) molecular dynamics (MD) simulations that resolve the ambiguity. The numerical evidence unequivocally favors the Juettner distribution. Moreover, our simulations illustrate that the concept of 'thermal equilibrium' extends naturally to special relativity only if a many-particle system is spatially confined. They make evident that 'temperature' can be statistically defined and measured in an observer frame independent way.Comment: version accepted for publication (5 pages), part of the introduction modified, new figures, additional reference

Estimation of Mechanical Vibrations of the LHC Fast Magnetic Measurement System

Current installation of the Large Hadron Collider (LHC) particle accelerator at CERN has required the use of a harmonic coil magnetic measurement system to quantify the magnetic field harmonic quality of the superconducting, twin aperture LHC dipoles. Current and future needs for measuring fast changing magnetic fields necessitates the use of a rotating unit (RU) and associated electronics to drive this long shaft with increased speed and measurement bandwidth. Therefore, the Fast Magnetic Measurement Equipment (FAME) project has been launched to deliver such a system. A primary obstacle to achieving the goals of the FAME project is the possibility of amplifying mechanical vibrations due to increased speeds. This paper presents the methodology and results of an experimental investigation conducted to estimate mechanical vibrations of the long shaft within a cold-bore mounted anti-cryostat at various rotational speeds using magnetic measurements

Hydrodynamic length-scale selection in microswimmer suspensions

A universal characteristic of mesoscale turbulence in active suspensions is the emergence of a typical vortex length scale, distinctly different from the scale invariance of turbulent high-Reynolds number flows. Collective length-scale selection has been observed in bacterial fluids, endothelial tissue, and active colloids, yet the physical origins of this phenomenon remain elusive. Here, we systematically derive an effective fourth-order field theory from a generic microscopic model that allows us to predict the typical vortex size in microswimmer suspensions. Building on a self-consistent closure condition, the derivation shows that the vortex length scale is determined by the competition between local alignment forces, rotational diffusion, and intermediate-range hydrodynamic interactions. Vortex structures found in simulations of the theory agree with recent measurements in Bacillus subtilis suspensions. Moreover, our approach yields an effective viscosity enhancement (reduction), as reported experimentally for puller (pusher) microorganisms

The Simple Non-degenerate Relativistic Gas: Statistical Properties and Brownian Motion

This paper shows a novel calculation of the mean square displacement of a classical Brownian particle in a relativistic thermal bath. The result is compared with the expressions obtained by other authors. Also, the thermodynamic properties of a non-degenerate simple relativistic gas are reviewed in terms of a treatment performed in velocity space.Comment: 6 pages, 2 figure

Formation of the planet around the millisecond pulsar J1719-1438

Context. Recently the discovery of PSR J1719-1438, a 5.8 ms pulsar with a companion in a 2.2 hr orbit, was reported. The combination of this orbital period and the very low mass function is unique. The discoverers, Bailes et al., proposed an ultracompact X-ray binary (UCXB) as the progenitor system. However, the standard UCXB scenario would not produce this system as the time required to reach this orbital period exceeds the current estimate of the age of the Universe. The detached state of the system aggravates the problem. Aims. We want to understand the evolutionary history of PSR J1719-1438, and determine under which circumstances it could have evolved from an UCXB. Methods. We model UCXB evolution varying the donor size and investigate the effect of a wind mass loss from the donor, and compare the results with the observed characteristics of PSR J1719-1438. Results. An UCXB can reach a 2.2 hr orbit within the age of the Universe, provided that 1) the millisecond pulsar can significantly heat and expand the donor by pulsar irradiation, or 2) the system loses extra orbital angular momentum, e.g. via a fast wind from the donor. Conclusions. The most likely scenario for the formation of PSR J1719-1438 is UCXB evolution driven by angular momentum loss via the usual gravitational wave emission, which is enhanced by angular momentum loss via a donor wind of ~3x10^-13 Msun/yr. Depending on the size of the donor during the evolution, the companion presently probably has a mass of ~1-3 Jupiter masses, making it a very low mass white dwarf as proposed by Bailes et al. Its composition can be either helium or carbon-oxygen. A helium white dwarf companion makes the long (for an UCXB) orbital period easier to explain, but the required inclination makes it a priori less likely than a carbon-oxygen white dwarf.Comment: 5 pages, 4 figures. Accepted for publication in Astronomy and Astrophysics. v2: Updated a referenc

A System for Series Magnetic Measurements of the LHC Main Quadrupoles

More than 400 twin aperture lattice quadrupoles are needed for the Large Hadron Collider (LHC) which is under construction at CERN. The main quadrupole is assembled with correction magnets in a common cryostat called the Short Straight Section (SSS). We plan to measure all SSS's in cold conditions with an unprecedented accuracy: integrated gradient of the field within 150 ppm, harmonics in a range of 1 to 5 ppm, magnetic axis of all elements within 0.1 mm and their field direction within 0.2 mrad. In this paper we describe the automatic measurement system that we have designed, built and calibrated. Based on the results obtained on the two first prototypes of the SSS's (SSS3 and SSS4) we show that this system meets all above requirements

Relativistic diffusion processes and random walk models

The nonrelativistic standard model for a continuous, one-parameter diffusion process in position space is the Wiener process. As well-known, the Gaussian transition probability density function (PDF) of this process is in conflict with special relativity, as it permits particles to propagate faster than the speed of light. A frequently considered alternative is provided by the telegraph equation, whose solutions avoid superluminal propagation speeds but suffer from singular (non-continuous) diffusion fronts on the light cone, which are unlikely to exist for massive particles. It is therefore advisable to explore other alternatives as well. In this paper, a generalized Wiener process is proposed that is continuous, avoids superluminal propagation, and reduces to the standard Wiener process in the non-relativistic limit. The corresponding relativistic diffusion propagator is obtained directly from the nonrelativistic Wiener propagator, by rewriting the latter in terms of an integral over actions. The resulting relativistic process is non-Markovian, in accordance with the known fact that nontrivial continuous, relativistic Markov processes in position space cannot exist. Hence, the proposed process defines a consistent relativistic diffusion model for massive particles and provides a viable alternative to the solutions of the telegraph equation.Comment: v3: final, shortened version to appear in Phys. Rev.