A short note on passivity, complete passivity and virtual temperatures

We give a simple and intuitive proof that the only states which are completely passive, i.e. those states from which work cannot be extracted even with infinitely many copies, are Gibbs states at positive temperatures. The proof makes use of the idea of virtual temperatures, i.e. the association of temperatures to pairs of energy levels (transitions). We show that (i) passive states are those where every transition is at a positive temperature, and (ii) completely passive states are those where every transition is at the same positive temperature.Comment: 3 pages, no figures. v2: Published versio

Physical constraints on the coefficients of Fourier expansions in cylindrical coordinates

It is demonstrated that (i) the postulate of infinite differentiability in Cartesian coordinates and (ii) the physical assumption of regularity on the axis of a cylindrical coordinate system provide significant simplifying constraints on the coefficients of Fourier expansions in cylindrical coordinates. These constraints are independent of any governing equations. The simplification can provide considerable practical benefit for the analysis (especially numerical) of actual physical problems. Of equal importance, these constraints demonstrate that if A is any arbitrary physical vector, then the only finite Fourier terms of A_r and A_θ are those with m=1 symmetry. In the Appendix, it is further shown that postulate (i) may be inferred from a more primitive assumption, namely, the arbitrariness of the location of the cylindrical axis of the coordinate system

Distances and parallax bias in Gaia DR2

We derive Bayesian distances for all stars in the RV sample of Gaia DR2, and use the statistical method of Schoenrich, Binney & Asplund(2012) to validate the distances and test the Gaia parallaxes. In contrast to other methods, which rely on special sources, our method directly tests the distances to all stars in our sample. We find clear evidence for a near-linear trend of distance bias f with distance s, proving a parallax offset delta p. On average, we find delta p = -0.054 mas (parallaxes in Gaia DR2 need to be increased) when accounting for the parallax uncertainty under-estimate in the Gaia set (delta p = -0.048 mas on the raw parallax errors) with negligible formal error and a systematic uncertainty of about 0.006 mas. The value is in concordance with results from asteroseismic measurements, but differs from the much lower bias found on quasar samples. We further use our method to compile a comprehensive set of quality cuts in colour, apparent magnitude, and astrometric parameters. Last, we find that for this sample delta p appears to strongly depend on the parallax uncertainty sigma_p (when including the additional 0.043 mas) with a statistical confidence far in excess of 10\sigma and a proportionality factor close to 1, though the dependence varies somewhat with sigma_p. Correcting for the sigma_p dependence also resolves otherwise unexplained correlations of the offset with the number of observation periods n_{vis} and ecliptic latitude. Every study using Gaia DR2 parallaxes/distances should investigate the sensitivity of their results on the parallax biases described here and - for fainter samples - in the DR2 astrometry paper.Comment: 14 pages, 13 figures, accepted in MNRAS. The derived distances, as well as stellar positions and kinematics are found at https://zenodo.org/record/255780

A thermodynamic basis for prebiotic amino acid synthesis and the nature of the first genetic code

Of the twenty amino acids used in proteins, ten were formed in Miller's atmospheric discharge experiments. The two other major proposed sources of prebiotic amino acid synthesis include formation in hydrothermal vents and delivery to Earth via meteorites. We combine observational and experimental data of amino acid frequencies formed by these diverse mechanisms and show that, regardless of the source, these ten early amino acids can be ranked in order of decreasing abundance in prebiotic contexts. This order can be predicted by thermodynamics. The relative abundances of the early amino acids were most likely reflected in the composition of the first proteins at the time the genetic code originated. The remaining amino acids were incorporated into proteins after pathways for their biochemical synthesis evolved. This is consistent with theories of the evolution of the genetic code by stepwise addition of new amino acids. These are hints that key aspects of early biochemistry may be universal.Comment: 16 pages, 2 tables, 4 figures. Accepted for publication in Astrobiolog

Saliency-guided integration of multiple scans

we present a novel method..