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Measuring entropy production of a system directly from the experimental data is highly desirable since it gives a quantifiable measure of the time-irreversibility for non-equilibrium systems and can be used as a cost function to optimize the performance of the system. Although numerous methods are available to infer the entropy production of stationary systems, there are only a limited number of methods that have been proposed for time-dependent systems and, to the best of our knowledge, none of these methods have been applied to experimental systems. Herein, we develop a general non-invasive methodology to infer a lower bound on the mean total entropy production for arbitrary time-dependent continuous-state Markov systems in terms of the moments of the underlying state variables. The method gives surprisingly accurate estimates for the entropy production, both for theoretical toy models and for experimental bit erasure, even with a very limited amount of experimental data., Comment: 30 pages, 8 figures

Today's robotic laboratories for drones are housed in a large room. At times, they are the size of a warehouse. These spaces are typically equipped with permanent devices to localize the drones, e.g., Vicon Infrared cameras. Significant time is invested to fine-tune the localization apparatus to compute and control the position of the drones. One may use these laboratories to develop a 3D multimedia system with miniature sized drones configured with light sources. As an alternative, this brave new idea paper envisions shrinking these room-sized laboratories to the size of a cube or cuboid that sits on a desk and costs less than 10K dollars. The resulting Dronevision (DV) will be the size of a 1990s Television. In addition to light sources, its Flying Light Specks (FLSs) will be network-enabled drones with storage and processing capability to implement decentralized algorithms. The DV will include a localization technique to expedite development of 3D displays. It will act as a haptic interface for a user to interact with and manipulate the 3D virtual illuminations. It will empower an experimenter to design, implement, test, debug, and maintain software and hardware that realize novel algorithms in the comfort of their office without having to reserve a laboratory. In addition to enhancing productivity, it will improve safety of the experimenter by minimizing the likelihood of accidents. This paper introduces the concept of a DV, the research agenda one may pursue using this device, and our plans to realize one.

Symbolic regression with polynomial neural networks and polynomial neural ordinary differential equations (ODEs) are two recent and powerful approaches for equation recovery of many science and engineering problems. However, these methods provide point estimates for the model parameters and are currently unable to accommodate noisy data. We address this challenge by developing and validating the following Bayesian inference methods: the Laplace approximation, Markov Chain Monte Carlo (MCMC) sampling methods, and variational inference. We have found the Laplace approximation to be the best method for this class of problems. Our work can be easily extended to the broader class of symbolic neural networks to which the polynomial neural network belongs.

We investigate the dynamics of tracer particles in the random average process (RAP), a single-file system in one dimension. In addition to the position, every particle possesses an internal spin variable $\sigma (t)$ that can alternate between two values, $\pm 1$, at a constant rate $\gamma$. Physically, the value of $\sigma (t)$ dictates the direction of motion of the corresponding particle and for finite $\gamma$, every particle performs a non-Markovian active dynamics. Herein, we study the effect of this non-Markovianity in the fluctuations and correlations of the positions of tracer particles. We analytically show that the variance of the position of a tagged particle grows sub-diffusively as $\sim \zeta_{\text{q}} \sqrt{t}$ at large times for the quenched uniform initial condition. While this sub-diffusive growth is identical to that of the Markovian/non-persistent RAP, the coefficient $\zeta_{\text{q}} $ is rather different and bears the signature of the persistent motion of active particles through higher point correlations (unlike in the Markovian case). Similarly, for the annealed (steady state) initial condition, we find that the variance scales as $\sim \zeta_{\text{a}} \sqrt{t}$ at large times with coefficient $\zeta_{\text{a}} $ once again different from the non-persistent case. Although $\zeta_{\text{q}}$ and $\zeta_{\text{a}} $ both individually depart from their Markov counterparts, their ratio $\zeta_{\text{a}} / \zeta_{\text{q}}$ is still equal to $\sqrt{2}$, a condition observed for other diffusive single-file systems. This condition turns out to be true even in the strongly active regimes as corroborated by extensive simulations and calculations. Finally, we study the correlation between the positions of two tagged particles in both quenched uniform and annealed initial conditions. We verify all our analytic results by extensive numerical simulations., Comment: 38 pages, 13 figures

This article is part-I of a review of density-functional theory (DFT) that is the most widely used method for calculating electronic structure of materials. The accuracy and ease of numerical implementation of DFT methods has resulted in its extensive use for materials design and discovery and has thus ushered in the new field of computational material science. In this article we start with an introduction to Schr\"odinger equation and methods of its solutions. After presenting exact results for some well-known systems, difficulties encountered in solving the equation for interacting electrons are described. How these difficulties are handled using the variational principle for the energy to obtain approximate solutions of the Schr\"odinger equation is discussed. The resulting Hartree and Hartree-Fock theories are presented along with results they give for atomic and solid-state systems. We then describe Thomas-Fermi theory and its extensions which were the initial attempts to formulate many-electron problem in terms of electronic density of a system. Having described these theories, we introduce modern density functional theory by discussing Hohenberg-Kohn theorems that form its foundations. We then go on to discuss Kohn-Sham formulation of density-functional theory in its exact form. Next, local density approximation is introduced and solutions of Kohn-Sham equation for some representative systems, obtained using the local density approximation, are presented. We end part-I of the review describing the contents of part-II., Comment: 44 pages, 3 figures, 5 tables

This is the second and the final part of the review on density functional theory (DFT), referred to as DFT-II. In the first review, DFT-I, we have discussed wavefunction-based methods, their complexity, and the basic of density functional theory. In DFT-II, we focus on fundamentals of DFT and their implications for the betterment of the theory. We start our presentation with the exact DFT result followed by the concept of exchange-correlation (xc) or Fermi-Coulomb hole and its relation with xc energy functional. We also provide the exact conditions for the xc-hole, xc-energy and xc-potential along with their physical interpretation. Next, we describe the extension of DFT for non-integer numbers of electrons, the piecewise linearity of total energy and discontinuity of chemical potential at integer particle numbers, and derivative discontinuity of the xc potential, which has consequences on fundamental gap of solids. After that, we present how one obtain more accurate xc energy functionals by going beyond LDA. We discuss the gradient expansion approximation (GEA), generalized gradient approximation (GGA), and hybrid functional approaches to designing better xc energy functionals that give accurate total energies but fail to predict properties like the ionization potential and the band gap. Thus, we describe different methods of modeling these potentials and the results of their application for the calculation of the band gaps of different solids to highlight accuracy of different xc potential. Finally, we conclude with a glimpse on orbital-free density functional theory and the machine learning approach ., Comment: 41 pages, 4 figures, 4 table

Ca$_2$FeMnO$_6$ (CFMO) double perovskite was studied using first principles density functional theory and tight-binding (TB) Hamiltonian modeling using extended Hubbard model. We have shown by electronic structure analysis that charge- and magnetic-ordering are driven by charge disproportionation at low temperature caused by partial localization of O-$2p$ ligand holes at alternate Fe sites that creates Jahn-Teller distortion, which leads to metal to insulator transition (MIT) in CFMO. Our results suggests MIT was triggered by negative charge-transfer energy of self-hole doping, responsible for symmetry lowering transitions. Notably, the band-gap was found to fundamentally controlled by the strength of the charge-transfer energy, and not by the Mott-Hubbard interactions, which can be modeled by composition, pressure or stoichiometry modulations. The fundamental insights presented in this work will help understand similar physics and mechanisms in other class of perovskites and correlated metals., Comment: 7 pages, 4 figures