Thermodynamic work from operational principles

In recent years we have witnessed a concentrated effort to make sense of thermodynamics for small-scale systems. One of the main difficulties is to capture a suitable notion of work that models realistically the purpose of quantum machines, in an analogous way to the role played, for macroscopic machines, by the energy stored in the idealisation of a lifted weight. Despite of several attempts to resolve this issue by putting forward specific models, these are far from capturing realistically the transitions that a quantum machine is expected to perform. In this work, we adopt a novel strategy by considering arbitrary kinds of systems that one can attach to a quantum thermal machine and seeking for work quantifiers. These are functions that measure the value of a transition and generalise the concept of work beyond the model of a lifted weight. We do so by imposing simple operational axioms that any reasonable work quantifier must fulfil and by deriving from them stringent mathematical condition with a clear physical interpretation. Our approach allows us to derive much of the structure of the theory of thermodynamics without taking as a primitive the definition of work. We can derive, for any work quantifier, a quantitative second law in the sense of bounding the work that can be performed using some non-equilibrium resource by the work that is needed to create it. We also discuss in detail the role of reversibility and correlations in connection with the second law. Furthermore, we recover the usual identification of work with energy in degrees of freedom with vanishing entropy as a particular case of our formalism. Our mathematical results can be formulated abstractly and are general enough to carry over to other resource theories than quantum thermodynamics.Comment: 22 pages, 4 figures, axioms significantly simplified, more comprehensive discussion of relationship to previous approache

Global velocity field and bubbles in the BCD Mrk86

We have studied the velocity field of the Blue Compact Dwarf galaxy Mrk86 (NGC2537) using data provided by 14 long-slit optical spectra. This kinematical information is complemented with narrow-band ([OIII]5007A and Halpha) and broad-band (B, V, Gunn-r and K) imaging. The analysis of the galaxy global velocity field suggests that the ionized gas could be distributed in a rotating inclined disk, with projected central angular velocity of Omega=34 km/s/kpc. The comparison between the stellar, HI and modeled dark matter density profile, indicates that the total mass within its optical radius is dominated by the stellar component. Peculiarities observed in its velocity field can be explained by irregularities in the ionized gas distribution or local motions induced by star formation. Kinematical evidences for two expanding bubbles, Mrk86-B and Mrk86-C, are given. They show expanding velocities of 34 km/s and 17 km/s, Halpha luminosities of 3x10^38 erg/s and 1.7x10^39 erg/s, and physical radii of 374 and 120 pc, respectively. The change in the [SII]/Halpha, [NII]/Halpha, [OII]/[OIII] and [OIII]/Hbeta line ratios with the distance to the bubble precursor suggests a diminution in the ionization parameter and, in the case of Mrk86-B, an enhancement of the shock-excited gas emission. The optical-near-infrared colours of the bubble precursors are characteristic of low metallicity star forming regions (0.2 Zsun) with burst strengths of about 1 per cent in mass.Comment: 14 pages, 12 PostScript figures, accepted for publication in MNRAS, also available at ftp://cutrex.fis.ucm.es/pub/OUT/gil/PAPERS