Relative Entropy: Free Energy Associated with Equilibrium Fluctuations and Nonequilibrium Deviations

Using a one-dimensional macromolecule in aqueous solution as an illustration, we demonstrate that the relative entropy from information theory, $\sum_k p_k\ln(p_k/p_k^*)$, has a natural role in the energetics of equilibrium and nonequilibrium conformational fluctuations of the single molecule. It is identified as the free energy difference associated with a fluctuating density in equilibrium, and is associated with the distribution deviate from the equilibrium in nonequilibrium relaxation. This result can be generalized to any other isothermal macromolecular systems using the mathematical theories of large deviations and Markov processes, and at the same time provides the well-known mathematical results with an interesting physical interpretations.Comment: 5 page

Group VIII Coordination Chemistry of a Pincer-Type Bis(8-quinolinyl)amido Ligand

This paper provides an entry point to the coordination chemistry of the group VIII chemistry of the bis(8-quinolinyl)amine (BQA) ligand. In this context, mono- and disubstituted BQA complexes of iron, ruthenium, and osmium are described. For example, the low-spin bis-ligated Fe(III) complex [Fe(BQA)2][BPh4] has been prepared via amine addition to FeCl3 in the presence of a base and NaBPh4. Complexes featuring a single BQA ligand are more readily prepared for Ru and Os. Auxiliary ligands featuring a single BQA ligand, along with two other L-type donor ligands, allow for a variety of ligand types to occupy a sixth coordination site. Representative examples include the halide and pseudohalide complexes trans-(BQA)MX(PPh3)2 (M = Ru, Os; X = Cl, Br, N3, OTf), as well as the hydride and alkyl complexes trans-(BQA)RuH(PMe3)2 and trans-(BQA)RuMe(PMe3)2. Electrochemical studies are discussed that help to contextualize the BQA ligand with respect to its neutral counterpart 2,2′,2′′-terpyridine (terpy) in terms of electron-releasing character. Bidentate ligands have been explored in conjunction with the BQA ligand. Thus, the bidentate, monoanionic aryl(8-quinolinyl)amido ligand 3,5-(CF3)2-(C6H3)QA has been installed onto the (BQA)Ru platform to provide (BQA)Ru(3,5-(CF3)2-(C6H3)QA)(PPh3). A bis(phosphino)borate ligand stabilizes the five-coordinate complex [Ph2B(CH2PPh2)2]Ru(BQA). Finally, access to dinitrogen complexes of the types [(BQA)Ru(N2)(PPh3)2][PF6], [(BQA)Ru(N2)(PMe3)2][PF6], and [(BQA)Os(N2)(PPh3)2][PF6] is provided by exposure of the sixth coordination site under a N2 atmosphere

Linear mixed models with endogenous covariates: modeling sequential treatment effects with application to a mobile health study

Mobile health is a rapidly developing field in which behavioral treatments are delivered to individuals via wearables or smartphones to facilitate health-related behavior change. Micro-randomized trials (MRT) are an experimental design for developing mobile health interventions. In an MRT the treatments are randomized numerous times for each individual over course of the trial. Along with assessing treatment effects, behavioral scientists aim to understand between-person heterogeneity in the treatment effect. A natural approach is the familiar linear mixed model. However, directly applying linear mixed models is problematic because potential moderators of the treatment effect are frequently endogenous---that is, may depend on prior treatment. We discuss model interpretation and biases that arise in the absence of additional assumptions when endogenous covariates are included in a linear mixed model. In particular, when there are endogenous covariates, the coefficients no longer have the customary marginal interpretation. However, these coefficients still have a conditional-on-the-random-effect interpretation. We provide an additional assumption that, if true, allows scientists to use standard software to fit linear mixed model with endogenous covariates, and person-specific predictions of effects can be provided. As an illustration, we assess the effect of activity suggestion in the HeartSteps MRT and analyze the between-person treatment effect heterogeneity

Field Induced Positional Shift of Bloch Electrons and its Dynamical Implications

We derive the field correction to the Berry curvature of Bloch electrons, which can be traced back to a positional shift due to the interband mixing induced by external electromagnetic fields. The resulting semiclassical dynamics is accurate to second order in the fields, in the same form as before, provided that the wave packet energy is derived up to the same order. As applications, we discuss the orbital magnetoelectric polarizability and predict nonlinear anomalous Hall effects

Rethinking Secure Precoding via Interference Exploitation: A Smart Eavesdropper Perspective

Based on the concept of constructive interference (CI), multiuser interference (MUI) has recently been shown to be beneficial for communication secrecy. A few CI-based secure precoding algorithms have been proposed that use both the channel state information (CSI) and knowledge of the instantaneous transmit symbols. In this paper, we examine the CI-based secure precoding problem with a focus on smart eavesdroppers that exploit statistical information gleaned from the precoded data for symbol detection. Moreover, the impact of correlation between the main and eavesdropper channels is taken into account. We first modify an existing CI-based preocding scheme to better utilize the destructive impact of the interference. Then, we point out the drawback of both the existing and the new modified CI-based precoders when faced with a smart eavesdropper. To address this deficiency, we provide a general principle for precoder design and then give two specific design examples. Finally, the scenario where the eavesdropper's CSI is unavailable is studied. Numerical results show that although our modified CI-based precoder can achieve a better energy-secrecy trade-off than the existing approach, both have a limited secrecy benefit. On the contrary, the precoders developed using the new CI-design principle can achieve a much improved trade-off and significantly degrade the eavesdropper's performance