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

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

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

Scattering fingerprints of two-state dynamics

Particle transport in complex environments such as the interior of living cells is often (transiently) non-Fickian or anomalous, that is, it deviates from the laws of Brownian motion. Such anomalies may be the result of small-scale spatio-temporal heterogeneities in, or viscoelastic properties of, the medium, molecular crowding, etc. Often the observed dynamics displays multi-state characteristics, i.e. distinct modes of transport dynamically interconverting between each other in a stochastic manner. Reliably distinguishing between single- and multi-state dynamics is challenging and requires a combination of distinct approaches. To complement the existing methods relying on the analysis of the particle's mean squared displacement, position- or displacement-autocorrelation function, and propagators, we here focus on 'scattering fingerprints' of multi-state dynamics. We develop a theoretical framework for two-state scattering signatures—the intermediate scattering function and dynamic structure factor—and apply it to the analysis of simple model systems as well as particle-tracking experiments in living cells. We consider inert tracer-particle motion as well as systems with an internal structure and dynamics. Our results may generally be relevant for the interpretation of state-of-the-art differential dynamic microscopy experiments on complex particulate systems, as well as inelastic or quasielastic neutron (incl. spin-echo) and x-ray scattering probing structural and dynamical properties of macromolecules, when the underlying dynamics displays two-state transport

Deep near-IR observations of the Globular Cluster M4: Hunting for Brown Dwarfs

We present an analysis of deep HST/WFC3 near-IR (NIR) imaging data of the globular cluster M4. The best-photometry NIR colour-magnitude diagram (CMD) clearly shows the main sequence extending towards the expected end of the Hydrogen-burning limit and going beyond this point towards fainter sources. The white dwarf sequence can be identified. As such, this is the deepest NIR CMD of a globular cluster to date. Archival HST optical data were used for proper-motion cleaning of the CMD and for distinguishing the white dwarfs (WDs) from brown dwarf (BD) candidates. Detection limits in the NIR are around F110W approx 26.5 mag and F160W approx27 mag, and in the optical around F775W approx 28 mag. Comparing our observed CMDs with theoretical models, we conclude that we have reached beyond the H-burning limit in our NIR CMD and are probably just above or around this limit in our optical-NIR CMDs. Thus, any faint NIR sources that have no optical counterpart are potential BD candidates, since the optical data are not deep enough to detect them. We visually inspected the positions of NIR sources which are fainter than the H-burning limit in F110W and for which the optical photometry did not return a counterpart. We found in total five sources for which we did not get an optical measurement. For four of these five sources, a faint optical counterpart could be visually identified, and an upper optical magnitude was estimated. Based on these upper optical magnitude limits, we conclude that one source is likely a WD, one source could either be a WD or BD candidate, and the remaining two sources agree with being BD candidates. For only one source no optical counterpart could be detected, which makes this source a good BD candidate. We conclude that we found in total four good BD candidates.Comment: ApJ accepted, 28 pages including 16 figure

Erupting Cataclysmic Variable Stars in the Nearest Globular Cluster, NGC 6397: Intermediate Polars?

NGC 6397 is the closest globular cluster, and hence the ideal place to search for faint stellar populations such as cataclysmic variables (CVs). HST and Chandra observers have identified nine certain and likely CVs in this nearby cluster, including several magnetic CV candidates. We have combined our recent UV imagery with archival HST images of NGC 6397 to search for new CV candidates and especially to look for dwarf nova-like eruptive events. We find remarkable and somewhat unexpected dwarf nova-like eruptions of the two well-known cataclysmic systems CV2 and CV3. These two objects have been claimed to be {\it magnetic} CVs, as indicated by their helium emission-line spectra. Magnetic fields in CVs are usually expected to prevent the disk instability that leads to dwarf nova eruptions. In fact, most field magnetic CVs are observed to not undergo eruptions. Our observations of the dwarf nova eruptions of CV2 and CV3 can be reconciled with these objects' HeII emission lines if both objects are infrequently-erupting intermediate polars, similar to EX Hya. If this is the case for most globular cluster CVs then we can reconcile the many X-ray and UV bright CV candidates seen by Chandra and HST with the very small numbers of erupting dwarf novae observed in cluster cores.Comment: 12 pages, 3 figures. Accepted for publication in The Astronomical Journal. Two additional authors adde

Astrophysical properties of binary star clusters in the Small Magellanic Cloud

To study the evolution of binary star clusters we have imaged 7 systems in the Small Magellanic Cloud with SOAR 4-m telescope using B and V filters. The sample contains pairs with well-separated components (d < 30 pc) as well as systems that apparently merged, as evidenced by their unusual structures. By employing isochrone fittings to their CMDs we have determined reddening, age and metallicity and by fitting King models to their radial stellar density profile we have estimated core radius. Disturbances of the density profile are interpreted as an evidence of interaction. Circunstances as distances between components and their age difference are addressed in terms of the timescales involved to access the physical connection of the system. In two cases the age difference is above 50 Myr, which suggests chance alignment, capture or sequential star formation.Comment: 4 pages, 1 figure. To appear in online version of Proc. IAU Symp. 266 (Star clusters), eds. R. de Grijs and J. Lepin