Non-invasive estimation of dissipation from non-equilibrium fluctuations in chemical reactions

We show how to extract from a sufficiently long time series of stationary fluctuations of chemical reactions an estimate of the entropy production. This method, which is based on recent work on fluctuation theorems, is direct, non-invasive, does not require any knowledge about the underlying dynamics, and is applicable even when only partial information is available. We apply it to simple stochastic models of chemical reactions involving a finite number of states, and for this case, we study how the estimate of dissipation is affected by the degree of coarse-graining present in the input data.Comment: Accepted in Journal of Chemical Physic

Time auto-correlation function and Green-Kubo formula: A study on disordered harmonic chain

We have considered heat conduction in a one-dimensional mass disordered harmonic chain of $N$ particles connected to two Langevin type reservoirs at different temperatures. An exact expression for the boundary heat current-current auto-correlation function in the non-equilibrium steady state (NESS) is obtained in terms of non-equilibrium phonon Green's functions. The time integral of the correlation function gives expected result, both in non-equilibrium as well as equilibrium cases. Using the form of this correlation function we show that asymptotic system size dependence of current fluctuation in NESS for a mass disordered harmonic chain is $N^{-\alpha}$ for different boundary conditions. For free and fixed boundary conditions we get $\alpha=1/2$ and 3/2 respectively, while for pinned case the fluctuation decays exponentially with system size

Yang-Baxter algebra and generation of quantum integrable models

An operator deformed quantum algebra is discovered exploiting the quantum Yang-Baxter equation with trigonometric R-matrix. This novel Hopf algebra along with its $q \to 1$ limit appear to be the most general Yang-Baxter algebra underlying quantum integrable systems. Three different directions of application of this algebra in integrable systems depending on different sets of values of deforming operators are identified. Fixed values on the whole lattice yield subalgebras linked to standard quantum integrable models, while the associated Lax operators generate and classify them in an unified way. Variable values construct a new series of quantum integrable inhomogeneous models. Fixed but different values at different lattice sites can produce a novel class of integrable hybrid models including integrable matter-radiation models and quantum field models with defects, in particular, a new quantum integrable sine-Gordon model with defect.Comment: 13 pages, revised and bit expanded with additional explanations, accepted for publication in Theor. Math. Phy

A Variable Black Hole X-Ray Source in a NGC 1399 Globular Cluster

We have discovered an accreting black hole (BH) in a spectroscopically confirmed globular cluster (GC) in NGC 1399 through monitoring of its X-ray activity. The source, with a peak luminosity of L_x=2x10^39 ergs/s, reveals an order of magnitude change in the count rate within ~10 ks in a Chandra observation. The BH resides in a metal-rich [Fe/H]~0.2 globular cluster. After RZ2109 in NGC 4472 this is only the second black-hole X-ray source in a GC confirmed via rapid X-ray variability. Unlike RZ2109, the X-ray spectrum of this BH source did not change during the period of rapid variability. In addition to the short-term variability the source also exhibits long-term variability. After being bright for at least a decade since 1993 within a span of 2 years it became progressively fainter, and eventually undetectable, or marginally detectable, in deep Chandra and XMM observations. The source also became harder as it faded. The characteristics of the long term variability in itself provide sufficient evidence to identify the source as a BH. The long term decline in the luminosity of this object was likely not recognized in previous studies because the rapid variability within the bright epoch suppressed the average luminosity in that integration. The hardening of the spectrum accompanying the fading would also make this black hole source indistinguishable from an accreting neutron star in some epochs. Therefore some low mass X-ray binaries identified as NS accretors in snapshot studies of nearby galaxies may also be BHs. Thus the discovery of the second confirmed BH in an extragalactic GC through rapid variability at the very least suggests that accreting BHs in GCs are not exceedingly rare occurences.Comment: 8 pages, 2 figs. Accepted for publication in Ap