Continuity bounds on observational entropy and measured relative entropies

We derive a measurement-independent asymptotic continuity bound on the observational entropy for general POVM measurements, making essential use of its property of bounded concavity. The same insight is used to obtain continuity bounds for other entropic quantities, including the measured relative entropy distance to a convex a set of states under a general set of measurements. As a special case, we define and study conditional observational entropy, which is an observational entropy in one (measured) subsystem conditioned on the quantum state in another (unmeasured) subsystem. We also study continuity of relative entropy with respect to a jointly applied channel, finding that observational entropy is uniformly continuous as a function of the measurement. But we show by means of an example that this continuity under measurements cannot have the form of a concrete asymptotic bound.Comment: 16 pages; v2 new Corollary 15 on measurement continuit

How young are early-type cluster galaxies ? Quantifying the young stellar component in a rich cluster at z=0.41

We present a new method of quantifying the mass fraction of young stars in galaxies by analyzing near-ultraviolet (NUV)-optical colors. We focus our attention on early-type cluster galaxies, whose star formation history is at present undetermined. Rest-frame NUV (F300W) and optical (F702W) images of cluster Abell 851 (z=0.41) using HST/WFPC2 allow us to determine a NUV-optical color-magnitude relation, whose slope is incompatible with a monolithic scenario for star formation at high redshift. A degeneracy between a young stellar component and its fractional mass contribution to the galaxy is found, and a photometric analysis comparing the data with the predictions for a simple two-stage star formation history is presented. The analysis shows that some of the early-type galaxies may have fractions higher than 10% of the total mass content in stars formed at z~0.5. An increased scatter is found in the color-magnitude relation at the faint end, resulting in a significant fraction of faint blue early-type systems. This would imply that less massive galaxies undergo more recent episodes of star formation, and this can be explained in terms of a positive correlation between star formation efficiency and luminosity.Comment: Accepted for publication in ApJ Letters. Uses emulateapj.sty. 5 pages with 3 embedded EPS figure

Observational entropy, coarse quantum states, and Petz recovery: information-theoretic properties and bounds

Observational entropy provides a general notion of quantum entropy that appropriately interpolates between Boltzmann's and Gibbs' entropies, and has recently been argued to provide a useful measure of out-of-equilibrium thermodynamic entropy. Here we study the mathematical properties of observational entropy from an information-theoretic viewpoint, making use of recently strengthened forms of the monotonicity property of quantum relative entropy. We present new bounds on observational entropy applying in general, as well as bounds and identities related to sequential and post-processed measurements. A central role in this work is played by what we call the ``coarse-grained'' state, which emerges from the measurement's statistics by Bayesian retrodiction, without presuming any knowledge about the ``true'' underlying state being measured. The degree of distinguishability between such a coarse-grained state and the true (but generally unobservable) one is shown to provide upper and lower bounds on the difference between observational and von Neumann entropies.Comment: 18 pages, 1 figure. v2 Greatly revised and restructured, adds new results. Questions and comments welcom

Particle-conserving dynamics on the single-particle level

We generalize the particle-conserving dynamics method of de las Heras et al. [J. Phys.: Condens. Matter 28, 244024 (2016)] to binary mixtures and apply this to hard rods in one dimension. Considering the case of one species consisting of only one particle enables us to address the tagged-particle dynamics. The time-evolution of the species-labeled density profiles is compared to exact Brownian dynamics and (grand- canonical) dynamical density functional theory. The particle-conserving dynamics yields improved results over the dynamical density functional theory and well reproduces the simulation data at short and intermediate times. However, the neglect of a strict particle order (due to the fundamental statistical assumption of ergodicity) leads to errors at long times for our one-dimensional setup. The isolated study of that error makes clear the fundamental limitations of (adiabatic) density-based theoretical approaches when applied to systems of any dimension for which particle caging is a dominant physical mechanism

The Structure of Evaporating Black Holes

A detailed model is constructed for the spacetime of an evaporating black hole. This model is used to analyze some persistent questions about black hole spacetimes in general, and to discuss the mechanism of Hawking radiation. The self-consistency of the model is studied and used to illuminate some general principles in semiclassical gravity. Along the way, a unified analysis is provided for the class of ``strongly spherically symmetric'' spacetimes, and a method for constructing a broad class of explicit Penrose diagrams is obtained