A Far-UV Variability Survey of the Globular Cluster M80

We have searched for variable sources in the core region of M80, using far ultra-violet data taken with the Advanced Camera for Surveys on board the Hubble Space Telescope. We found three sources that exhibit strong signs of variability in our data. Among these is source TDK1, which we believe to be an RR Lyrae star that reached maximum brightness during our observations. The light curve shows a >3 mag FUV brightening over the course of ~5 hours, with an estimated peak brightness of ~16.7 mag, followed by a decrease to ~20 mag. Archival optical data obtained with WFPC2 confirm that TDK1 is variable in all wavebands. TDK1's SED is reasonably fit by a star with temperature T(eff)=6700K and radius R=4.2R(sun), consistent with the suggestion that it is an RR Lyrae. Based on the photometric and variability characteristics of the other two variables, we suggest that TDK2 is likely to be an SX Phoenicis star with ~55 minutes period, and TDK3 is likely another RR Lyrae. Finally, we briefly discuss the FUV counterparts to two previously known variables in M80, the classical nova T Sco and the dwarf nova DN1.Comment: 12 pages, 9 figures and 3 tables. Accepted for publication in MNRAS

The ultraviolet colour of globular clusters in M31: a core density effect?

We investigate the effect of stellar density on the ultraviolet (UV) emission from M31's globular clusters (GCs). Published far-UV (FUV) and near-UV (NUV) colours from Galaxy Evolution and Explorer (GALEX) observations are used as a probe into the temperature of the horizontal branch (HB) stars in these clusters. From these data, we demonstrate a significant relationship between the core density of a cluster and its FUV-NUV colour, with dense clusters having bluer ultraviolet colours. These results are consistent with a population of (FUV bright) extreme-HB (EHB) stars, the production of which is related to the stellar density in the clusters. Such a relationship may be expected if the formation of EHB stars is enhanced in dense clusters due to dynamical interactions. We also consider the contribution of low mass X-ray binaries (LMXBs) to the integrated FUV luminosity of a cluster. We note that two of the three metal rich clusters, identified by Rey et al. 2007 as having a FUV excess, are known to host LMXBs in outburst. Considering the FUV luminosity of Galactic LMXBs, we suggest that a single LMXB is unlikely to produce more than 10% of the observed FUV luminosity of clusters that contain a significant population of blue-HB stars.Comment: Accepted for publication in MNRAS, 9 pages, 6 figures and 1 tabl

Feynman-Kac theory of time-integrated functionals: Itô versus functional calculus

The fluctuations of dynamical functionals such as the empirical density and current as well as heat, work and generalized currents in stochastic thermodynamics are often studied within the Feynman-Kac tilting formalism, which in the physics literature is typically derived by some form of Kramers-Moyal expansion. Here we derive the Feynman-Kac theory for general additive dynamical functionals directly via Itô calculus and via functional calculus, where the latter approach in fact appears to be new. Using Dyson series we then independently recapitulate recent results on steady-state (co)variances of general additive dynamical functionals derived in arXiv:2105.10483 and arXiv:2204.06553 directly from Itô calculus avoiding any tilting. We hope for our work to put the different approaches to stochastic functionals employed in the field on a common footing

Direct Route to Thermodynamic Uncertainty Relations

Thermodynamic uncertainty relations (TURs) bound the dissipation in non-equilibrium systems from below by fluctuations of an observed current. Contrasting the elaborate techniques employed in existing proofs, we here prove TURs directly from the Langevin equation. This establishes the TUR as an inherent property of overdamped stochastic equations of motion. By including current-density correlations we, moreover, derive a new sharpened TUR for transient dynamics. Our arguably simplest and most direct proof allows us to systematically determine conditions under which the different TURs saturate and thus allows for a more accurate thermodynamic inference

Feynman-Kac theory of time-integrated functionals: It\^o versus functional calculus

The fluctuations of dynamical functionals such as the empirical density and current as well as heat, work and generalized currents in stochastic thermodynamics are usually studied within the Feynman-Kac tilting formalism, which in the Physics literature is typically derived by some form of Kramers-Moyal expansion, or in the Mathematical literature via the Cameron-Martin-Girsanov approach. Here we derive the Feynman-Kac theory for general additive dynamical functionals directly via It\^o calculus and via functional calculus, where the latter result in fact appears to be new. Using Dyson series we then independently recapitulate recent results on steady-state (co)variances of general additive dynamical functionals derived recently in Dieball and Godec ({2022 \textit{Phys. Rev. Lett.}~\textbf{129} 140601}) and Dieball and Godec ({2022 \textit{Phys. Rev. Res.}~\textbf{4} 033243}). We hope for our work to put the different approaches to the statistics of dynamical functionals employed in the field on a common footing, and to illustrate more easily accessible ways to the tilting formalism

Mathematical, Thermodynamical, and Experimental Necessity for Coarse Graining Empirical Densities and Currents in Continuous Space

We present general results on fluctuations and spatial correlations of the coarse-grained empirical density and current of Markovian diffusion in equilibrium or non-equilibrium steady states on all time scales. We unravel a deep connection between current fluctuations and generalized time-reversal symmetry, providing new insight into time-averaged observables. We highlight the essential role of coarse graining in space from mathematical, thermodynamical, and experimental points of view. Spatial coarse graining is required to uncover salient features of currents that break detailed balance, and a thermodynamically "optimal" coarse graining ensures the most precise inference of dissipation. Defined without coarse graining, the fluctuations of empirical density and current are proven to diverge on all time scales in dimensions higher than one, which has far-reaching consequences for the central-limit regime in continuous space. We apply the results to examples of irreversible diffusion. Our findings provide new intuition about time-averaged observables and allow for a more efficient analysis of single-molecule experiments.Comment: Version accepted for publication in Physical Review Letter

On correlations and fluctuations of time-averaged densities and currents with general time-dependence

We present technical results required for the description and understand- ing of correlations and fluctuations of the empirical density and current as well as diverse time-integrated and time-averaged thermodynamic currents of diffusion pro- cesses with a general time dependence on all time scales. In particular, we generalize the results from arXiv:2105.10483 (Phys. Rev. Lett. , article in press), arXiv:2204.06553 (Phys. Rev. Research, article in press), and arXiv:2206.04034 to additive functionals with explicit time dependence and transient or non-ergodic overdamped diffusion. As an illustration we apply the results to two-dimensional harmonically confined over- damped diffusion in a rotational flow evolving from a non-stationary initial distribution

Coarse graining empirical densities and currents in continuous-space steady states

We present the conceptual and technical background required to describe and understand the correlations and fluctuations of the empirical density and current of steady-state diffusion processes on all time scales — observables central to statistical mechanics and thermodynamics on the level of individual trajectories. We focus on the important and non-trivial effect of a spatial coarse graining. Making use of a generalized time-reversal symmetry we provide deeper insight about the physical meaning of fluctuations of the coarse-grained empirical density and current, and explain why a systematic variation of the coarse-graining scale offers an efficient method to infer bounds on a system’s dissipation. Moreover, we discuss emerging symmetries in the statistics of the empirical density and current, and the statistics in the large deviations regime. More broadly our work promotes the application of stochastic calculus as a powerful direct alternative to Feynman-Kac theory and path-integral methods