Surface charge algebra in gauge theories and thermodynamic integrability

Surface charges and their algebra in interacting Lagrangian gauge field theories are investigated by using techniques from the variational calculus. In the case of exact solutions and symmetries, the surface charges are interpreted as a Pfaff system. Integrability is governed by Frobenius' theorem and the charges associated with the derived symmetry algebra are shown to vanish. In the asymptotic context, we provide a generalized covariant derivation of the result that the representation of the asymptotic symmetry algebra through charges may be centrally extended. Finally, we make contact with Hamiltonian and with covariant phase space methods.Comment: 40 pages Latex file, published versio

Covariant Hamiltonian Field Theory

A consistent, local coordinate formulation of covariant Hamiltonian field theory is presented. Whereas the covariant canonical field equations are equivalent to the Euler-Lagrange field equations, the covariant canonical transformation theory offers more general means for defining mappings that preserve the form of the field equations than the usual Lagrangian description. It is proved that Poisson brackets, Lagrange brackets, and canonical 2-forms exist that are invariant under canonical transformations of the fields. The technique to derive transformation rules for the fields from generating functions is demonstrated by means of various examples. In particular, it is shown that the infinitesimal canonical transformation furnishes the most general form of Noether's theorem. We furthermore specify the generating function of an infinitesimal space-time step that conforms to the field equations.Comment: 93 pages, no figure

Irreversible thermodynamics of open chemical networks I: Emergent cycles and broken conservation laws

In this and a companion paper we outline a general framework for the thermodynamic description of open chemical reaction networks, with special regard to metabolic networks regulating cellular physiology and biochemical functions. We first introduce closed networks "in a box", whose thermodynamics is subjected to strict physical constraints: the mass-action law, elementarity of processes, and detailed balance. We further digress on the role of solvents and on the seemingly unacknowledged property of network independence of free energy landscapes. We then open the system by assuming that the concentrations of certain substrate species (the chemostats) are fixed, whether because promptly regulated by the environment via contact with reservoirs, or because nearly constant in a time window. As a result, the system is driven out of equilibrium. A rich algebraic and topological structure ensues in the network of internal species: Emergent irreversible cycles are associated to nonvanishing affinities, whose symmetries are dictated by the breakage of conservation laws. These central results are resumed in the relation $a + b = s^Y$ between the number of fundamental affinities $a$, that of broken conservation laws $b$ and the number of chemostats $s^Y$. We decompose the steady state entropy production rate in terms of fundamental fluxes and affinities in the spirit of Schnakenberg's theory of network thermodynamics, paving the way for the forthcoming treatment of the linear regime, of efficiency and tight coupling, of free energy transduction and of thermodynamic constraints for network reconstruction.Comment: 18 page

Non-equilibrium Thermodynamics: Structural Relaxation, Fictive temperature and Tool-Narayanaswamy phenomenology in Glasses

Starting from the second law of thermodynamics applied to an isolated system consisting of the system surrounded by an extremely large medium, we formulate a general non-equilibrium thermodynamic description of the system when it is out of equilibrium. We then apply it to study the structural relaxation in glasses and establish the phenomenology behind the concept of the fictive temperature and of the empirical Tool-Narayanaswamy equation on firmer theoretical foundation.Comment: 20 pages, 1 figur

Fluctuation theorem and large deviation function for a solvable model of a molecular motor

We study a discrete stochastic model of a molecular motor. This discrete model can be viewed as a \emph{minimal} ratchet model. We extend our previous work on this model, by further investigating the constraints imposed by the Fluctuation Theorem on the operation of a molecular motor far from equilibrium. In this work, we show the connections between different formulations of the Fluctuation Theorem. One formulation concerns the generating function of the currents while another one concerns the corresponding large deviation function, which we have calculated exactly for this model. A third formulation of FT concerns the ratio of the probability of making one forward step to the probability of making one backward step. The predictions of this last formulation of the Fluctuation Theorem adapted to our model are in very good agreement with the data of Carter and Cross [Nature, {\bf 435}, 308 (2005)] on single molecule measurements with kinesin. Finally, we show that all the formulations of FT can be understood from the notion of entropy production.Comment: 15 pages, 9 figure

Search for an Near-IR Counterpart to the Cas A X-ray Point Source

We report deep near-infrared and optical observations of the X-ray point source in the Cassiopeia A supernova remnant, CXO J232327.9+584842. We have identified a J=21.4 +/- 0.3 mag and Ks=20.5 +/- 0.3 mag source within the 1-sigma error circle, but we believe this source is a foreground Pop II star with Teff=2600-2800 K at a distance of ~2 kpc, which could not be the X-ray point source. We do not detect any sources in this direction at the distance of Cas A, and therefore place 3-sigma limits of R >~ 25 mag, F675W >~ 27.3 mag, J >~ 22.5 mag and Ks >~ 21.2 mag (and roughly H >~ 20 mag) on emission from the X-ray point source, corresponding to M_{R} >~ 8.2 mag, M_{F675W} >~ 10.7 mag, M_{J} >~ 8.5 mag, M_{H} >~ 6.5 mag, and M_{Ks} >~ 8.0 mag, assuming a distance of 3.4 kpc and an extinction A_{V}=5 mag.Comment: 14 pages, 7 figures. Accepted by Ap

Excision boundary conditions for the conformal metric

Shibata, Ury\=u and Friedman recently suggested a new decomposition of Einstein's equations that is useful for constructing initial data. In contrast to previous decompositions, the conformal metric is no longer treated as a freely-specifiable variable, but rather is determined as a solution to the field equations. The new set of freely-specifiable variables includes only time-derivatives of metric quantities, which makes this decomposition very attractive for the construction of quasiequilibrium solutions. To date, this new formalism has only been used for binary neutron stars. Applications involving black holes require new boundary conditions for the conformal metric on the domain boundaries. In this paper we demonstrate how these boundary conditions follow naturally from the conformal geometry of the boundary surfaces and the inherent gauge freedom of the conformal metric.Comment: 10 pages, revtex4, accepted by Physical Review

Matched Asymptotic Expansion for Caged Black Holes - Regularization of the Post-Newtonian Order

The "dialogue of multipoles" matched asymptotic expansion for small black holes in the presence of compact dimensions is extended to the Post-Newtonian order for arbitrary dimensions. Divergences are identified and are regularized through the matching constants, a method valid to all orders and known as Hadamard's partie finie. It is closely related to "subtraction of self-interaction" and shows similarities with the regularization of quantum field theories. The black hole's mass and tension (and the "black hole Archimedes effect") are obtained explicitly at this order, and a Newtonian derivation for the leading term in the tension is demonstrated. Implications for the phase diagram are analyzed, finding agreement with numerical results and extrapolation shows hints for Sorkin's critical dimension - a dimension where the transition turns second order.Comment: 28 pages, 5 figures. v2:published versio

Effects of CPT and Lorentz Invariance Violation on Pulsar Kicks

The breakdown of Lorentz's and CPT invariance, as described by the Extension of the Standard Model, gives rise to a modification of the dispersion relation of particles. Consequences of such a modification are reviewed in the framework of pulsar kicks induced by neutrino oscillations (active-sterile conversion). A peculiar feature of the modified energy-momentum relations is the occurrence of terms of the form \delta {\bbox \Pi}\cdot {\bf {\hat p}}, where \delta {\bbox \Pi} accounts for the difference of spatial components of flavor depending coefficients which lead to the departure of the Lorentz symmetry, and ${\bf {\hat p}}={\bf p}/p$, being ${\bf p}$ the neutrino momentum. Owing to the relative orientation of ${\bf p}$ with respect to \delta {\bbox \Pi}, the {\it coupling} \delta {\bbox \Pi}\cdot {\bf {\hat p}} may induce the mechanism to generate the observed pulsar velocities. Topics related to the velocity distribution of pulsars are also discussed.Comment: 10 pages, 1 figur