@article{53474, abstract = {{We present a novel approach to characterize and quantify microheterogeneity and microphase separation in computer simulations of complex liquid mixtures. Our post-processing method is based on local density fluctuations of the different constituents in sampling spheres of varying size. It can be easily applied to both molecular dynamics (MD) and Monte Carlo (MC) simulations, including periodic boundary conditions. Multidimensional correlation of the density distributions yields a clear picture of the domain formation due to the subtle balance of different interactions. We apply our approach to the example of force field molecular dynamics simulations of imidazolium-based ionic liquids with different side chain lengths at different temperatures, namely 1-ethyl-3-methylimidazolium chloride, 1-hexyl-3-methylimidazolium chloride, and 1-decyl-3-methylimidazolium chloride, which are known to form distinct liquid domains. We put the results into the context of existing microheterogeneity analyses and demonstrate the advantages and sensitivity of our novel method. Furthermore, we show how to estimate the configuration entropy from our analysis, and we investigate voids in the system. The analysis has been implemented into our program package TRAVIS and is thus available as free software.}}, author = {{Lass, Michael and Kenter, Tobias and Plessl, Christian and Brehm, Martin}}, issn = {{1099-4300}}, journal = {{Entropy}}, number = {{4}}, publisher = {{MDPI AG}}, title = {{{Characterizing Microheterogeneity in Liquid Mixtures via Local Density Fluctuations}}}, doi = {{10.3390/e26040322}}, volume = {{26}}, year = {{2024}}, } @article{21820, abstract = {{The reduction of high-dimensional systems to effective models on a smaller set of variables is an essential task in many areas of science. For stochastic dynamics governed by diffusion processes, a general procedure to find effective equations is the conditioning approach. In this paper, we are interested in the spectrum of the generator of the resulting effective dynamics, and how it compares to the spectrum of the full generator. We prove a new relative error bound in terms of the eigenfunction approximation error for reversible systems. We also present numerical examples indicating that, if Kramers–Moyal (KM) type approximations are used to compute the spectrum of the reduced generator, it seems largely insensitive to the time window used for the KM estimators. We analyze the implications of these observations for systems driven by underdamped Langevin dynamics, and show how meaningful effective dynamics can be defined in this setting.}}, author = {{Nüske, Feliks and Koltai, Péter and Boninsegna, Lorenzo and Clementi, Cecilia}}, issn = {{1099-4300}}, journal = {{Entropy}}, title = {{{Spectral Properties of Effective Dynamics from Conditional Expectations}}}, doi = {{10.3390/e23020134}}, year = {{2021}}, } @article{21819, abstract = {{Many dimensionality and model reduction techniques rely on estimating dominant eigenfunctions of associated dynamical operators from data. Important examples include the Koopman operator and its generator, but also the Schrödinger operator. We propose a kernel-based method for the approximation of differential operators in reproducing kernel Hilbert spaces and show how eigenfunctions can be estimated by solving auxiliary matrix eigenvalue problems. The resulting algorithms are applied to molecular dynamics and quantum chemistry examples. Furthermore, we exploit that, under certain conditions, the Schrödinger operator can be transformed into a Kolmogorov backward operator corresponding to a drift-diffusion process and vice versa. This allows us to apply methods developed for the analysis of high-dimensional stochastic differential equations to quantum mechanical systems.}}, author = {{Klus, Stefan and Nüske, Feliks and Hamzi, Boumediene}}, issn = {{1099-4300}}, journal = {{Entropy}}, title = {{{Kernel-Based Approximation of the Koopman Generator and Schrödinger Operator}}}, doi = {{10.3390/e22070722}}, year = {{2020}}, } @article{53274, abstract = {{This paper studies the performance of improper Gaussian signaling (IGS) over a 2-user Rayleigh single-input single-output (SISO) interference channel, treating interference as noise. We assume that the receivers have perfect channel state information (CSI), while the transmitters have access to only statistical CSI. Under these assumptions, we consider a signaling scheme, which we refer to as proper/improper Gaussian signaling or PGS/IGS, where at most one user may employ IGS. For the Rayleigh fading channel model, we characterize the statistical distribution of the signal-to-interference-plus-noise ratio at each receiver and derive closed-form expressions for the ergodic rates. By adapting the powers, we characterize the Pareto boundary of the ergodic rate region for the 2-user fading IC. The ergodic transmission rates can be attained using fixed-rate codebooks and no optimization is involved. Our results show that, in the moderate and strong interference regimes, the proposed PGS/IGS scheme improves the performance with respect to the PGS scheme. Additionally, we numerically compute the ergodic rate region of the full IGS scheme when both users can employ IGS and their transmission parameters are optimized by an exhaustive search. Our results suggest that most of the Pareto optimal points for the 2-user fading IC channel are attained when either both users transmit PGS or when one transmits PGS and the other transmits maximally improper Gaussian signals and time sharing is allowed.}}, author = {{Soleymani, Mohammad and Santamaria, Ignacio and Lameiro, Christian and Schreier, Peter J.}}, issn = {{1099-4300}}, journal = {{Entropy}}, keywords = {{General Physics and Astronomy}}, number = {{10}}, publisher = {{MDPI AG}}, title = {{{Ergodic Rate for Fading Interference Channels with Proper and Improper Gaussian Signaling}}}, doi = {{10.3390/e21100922}}, volume = {{21}}, year = {{2019}}, }