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 analyze 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.Comment: 33 pages, 2 figures, substantial improvement of http://arxiv.org/abs/1308.674

Conformal Gauge Transformations in Thermodynamics

In this work we consider conformal gauge transformations of the geometric structure of thermodynamic fluctuation theory. In particular, we show that the Thermodynamic Phase Space is naturally endowed with a non-integrable connection, defined by all those processes that annihilate the Gibbs 1-form, i.e. reversible processes. Therefore the geometry of reversible processes is invariant under re-scalings, that is, it has a conformal gauge freedom. Interestingly, as a consequence of the non-integrability of the connection, its curvature is not invariant under conformal gauge transformations and, therefore, neither is the associated pseudo-Riemannian geometry. We argue that this is not surprising, since these two objects are associated with irreversible processes. Moreover, we provide the explicit form in which all the elements of the geometric structure of the Thermodynamic Phase Space change under a conformal gauge transformation. As an example, we revisit the change of the thermodynamic representation and consider the resulting change between the two metrics on the Thermodynamic Phase Space which induce Weinhold's energy metric and Ruppeiner's entropy metric. As a by-product we obtain a proof of the well-known conformal relation between Weinhold's and Ruppeiner's metrics along the equilibrium directions. Finally, we find interesting properties of the almost para-contact structure and of its eigenvectors which may be of physical interest

New phenomena in the standard no-scale supergravity model

We revisit the no-scale mechanism in the context of the simplest no-scale supergravity extension of the Standard Model. This model has the usual five-dimensional parameter space plus an additional parameter $\xi_{3/2}\equiv m_{3/2}/m_{1/2}$. We show how predictions of the model may be extracted over the whole parameter space. A necessary condition for the potential to be stable is ${\rm Str}{\cal M}^4>0$, which is satisfied if \bf m_{3/2}\lsim2 m_{\tilde q}. Order of magnitude calculations reveal a no-lose theorem guaranteeing interesting and potentially observable new phenomena in the neutral scalar sector of the theory which would constitute a ``smoking gun'' of the no-scale mechanism. This new phenomenology is model-independent and divides into three scenarios, depending on the ratio of the weak scale to the vev at the minimum of the no-scale direction. We also calculate the residual vacuum energy at the unification scale ($C_0\, m^4_{3/2}$), and find that in typical models one must require $C_0>10$. Such constraints should be important in the search for the correct string no-scale supergravity model. We also show how specific classes of string models fit within this framework.Comment: 11pages, LaTeX, 1 figure (included), CERN-TH.7433/9

Characterizing the radial oxygen abundance distribution in disk galaxies

We examine the possible dependence of the radial oxygen abundance distribution on non-axisymmetrical structures (bar/spirals) and other macroscopic parameters such as the mass, the optical radius R25, the color g-r, and the surface brightness of the galaxy. A sample of disk galaxies from the CALIFA DR3 is considered. We adopted the Fourier amplitude A2 of the surface brightness as a quantitative characteristic of the strength of non-axisymmetric structures in a galactic disk, in addition to the commonly used morphologic division for A, AB, and B types based on the Hubble classification. To distinguish changes in local oxygen abundance caused by the non-axisymmetrical structures, the multiparametric mass--metallicity relation was constructed as a function of parameters such as the bar/spiral pattern strength, the disk size, color index g-r in the SDSS bands, and central surface brightness of the disk. The gas-phase oxygen abundance gradient is determined by using the R calibration. We find that there is no significant impact of the non-axisymmetric structures such as a bar and/or spiral patterns on the local oxygen abundance and radial oxygen abundance gradient of disk galaxies. Galaxies with higher mass, however, exhibit flatter oxygen abundance gradients in units of dex/kpc, but this effect is significantly less prominent for the oxygen abundance gradients in units of dex/R25 and almost disappears when the inner parts are avoided. We show that the oxygen abundance in the central part of the galaxy depends neither on the optical radius R25 nor on the color g-r or the surface brightness of the galaxy. Instead, outside the central part of the galaxy, the oxygen abundance increases with g-r value and central surface brightness of the disk.Comment: 11 pages, 6 figures; accepted for publication in A&

On the radial distribution function of a hard-sphere fluid

Two related approaches, one fairly recent [A. Trokhymchuk et al., J. Chem. Phys. 123, 024501 (2005)] and the other one introduced fifteen years ago [S. B. Yuste and A. Santos, Phys. Rev. A 43, 5418 (1991)], for the derivation of analytical forms of the radial distribution function of a fluid of hard spheres are compared. While they share similar starting philosophy, the first one involves the determination of eleven parameters while the second is a simple extension of the solution of the Percus-Yevick equation. It is found that the {second} approach has a better global accuracy and the further asset of counting already with a successful generalization to mixtures of hard spheres and other related systems.Comment: 3 pages, 1 figure; v2: slightly shortened, figure changed, to be published in JC