arXiv subjects

Diego González

Publications and source records attributed to Diego González.

15 recordsLinked to original sources

arXiv2023

Classical analogs of generalized purities, entropies, and logarithmic negativity

It has recently been proposed classical analogs of the purity, linear quantum entropy, and von Neumann entropy for classical integrable systems, when the corresponding quantum system is in a Gaussian state. We generalized these results by providing classical analogs of the generalized purities, Bastiaans-Tsallis entropies, Rényi entropies, and logarithmic negativity for classical integrable systems. These classical analogs are entirely characterized by the classical covariance matrix. We compute these classical analogs exactly in the cases of linearly coupled harmonic oscillators, a generalized harmonic oscillator chain, and a one-dimensional circular lattice of oscillators. In all of these systems, the classical analogs reproduce the results of their quantum counterparts whenever the system is in a Gaussian state. In this context, our results show that quantum information of Gaussian states can be reproduced by classical information.

quant-ph↗

arXiv2022

Classical analogs of the covariance matrix, purity, linear entropy, and von Neumann entropy

We obtain a classical analog of the quantum covariance matrix by performing its classical approximation for any continuous quantum state, and we illustrate this approach with the anharmonic oscillator. Using this classical covariance matrix, we propose classical analogs of the purity, linear quantum entropy, and von Neumann entropy for classical integrable systems, when the quantum counterpart of the system under consideration is in a Gaussian state. As is well known, this matrix completely characterizes the purity, linear quantum entropy, and von Neumann entropy for Gaussian states. These classical analogs can be interpreted as quantities that reveal how much information from the complete system remains in the considered subsystem. To illustrate our approach, we calculate these classical analogs for three coupled harmonic oscillators and two linearly coupled oscillators. We find that they exactly reproduce the results of their quantum counterparts. In this sense, it is remarkable that we can calculate these quantities from the classical viewpoint.

quant-ph↗

arXiv2021

Detection of Maternal and Fetal Stress from the Electrocardiogram with Self-Supervised Representation Learning

In the pregnant mother and her fetus, chronic prenatal stress results in entrainment of the fetal heartbeat by the maternal heartbeat, quantified by the fetal stress index (FSI). Deep learning (DL) is capable of pattern detection in complex medical data with high accuracy in noisy real-life environments, but little is known about DL's utility in non-invasive biometric monitoring during pregnancy. A recently established self-supervised learning (SSL) approach to DL provides emotional recognition from electrocardiogram (ECG). We hypothesized that SSL will identify chronically stressed mother-fetus dyads from the raw maternal abdominal electrocardiograms (aECG), containing fetal and maternal ECG. Chronically stressed mothers and controls matched at enrolment at 32 weeks of gestation were studied. We validated the chronic stress exposure by psychological inventory, maternal hair cortisol and FSI. We tested two variants of SSL architecture, one trained on the generic ECG features for emotional recognition obtained from public datasets and another transfer-learned on a subset of our data. Our DL models accurately detect the chronic stress exposure group (AUROC=0.982+/-0.002), the individual psychological stress score (R2=0.943+/-0.009) and FSI at 34 weeks of gestation (R2=0.946+/-0.013), as well as the maternal hair cortisol at birth reflecting chronic stress exposure (0.931+/-0.006). The best performance was achieved with the DL model trained on the public dataset and using maternal ECG alone. The present DL approach provides a novel source of physiological insights into complex multi-modal relationships between different regulatory systems exposed to chronic stress. The final DL model can be deployed in low-cost regular ECG biosensors as a simple, ubiquitous early stress detection and monitoring tool during pregnancy. This discovery should enable early behavioral interventions.

q-bio.QM↗

arXiv2020

Revisiting the experimental test of Mermin's inequalities at IBMQ

Bell-type inequalities allow for experimental testing of local hidden variable theories. In the present work we show the violation of Mermin's inequalities in IBM's five-qubit quantum computers, ruling out the local realism hypothesis in quantum mechanics. Furthermore, our numerical results show significant improvement with respect to previous implementations. The circuit implementation of these inequalities is also proposed as a way of assessing the reliability of different quantum computers.

quant-ph↗

arXiv2020

Solving equations of motion by using Monte Carlo Metropolis: Novel method via Random Paths and Maximum Caliber Principle

A permanent challenge in physics and other disciplines is to solve partial differential equations, thereby a beneficial investigation is to continue searching for new procedures to do it. In this Letter, a novel Monte-Carlo Metropolis framework is presented for solving the equations of motion in Lagrangian systems. The implementation lies in sampling the paths space with a probability functional obtained by using the maximum caliber principle. The methodology was applied to the free particle and the harmonic oscillator problems, where the numerically-averaged path obtained from the Monte-Carlo simulation converges to the analytical solution from classical mechanics, in an analogous way with a canonical system where energy is minimized by sampling the state space and computing the average state for each system. Thus, we expect that this procedure can be general enough to solve other differential equations in physics and to be a useful tool to calculate the time-dependent properties of dynamical systems in order to understand the non-equilibrium behavior of statistical mechanical systems.

physics.comp-ph↗

arXiv2016

$BF$ gravity

$BF$ gravity comprises all the formulations of gravity that are based on deformations of $BF$ theory. Such deformations consist of either constraints or potential terms added to the topological $BF$ action that turn some of the gauge degrees of freedom into physical ones, particularly giving rise to general relativity. The $BF$ formulations have provided new and deep insights into many classical and quantum aspects of the gravitational field, setting the foundations for the approach to quantum gravity known as spinfoam models. In this review, we present a self-contained and unified treatment of the $BF$ formulations of $D$-dimensional general relativity and other related models, focusing on the classical aspects of them and including some new results.

gr-qc↗

arXiv2016

Jarzynski equality in the context of maximum path entropy

In the global framework of finding an axiomatic derivation of nonequilibrium Statistical Mechanics from fundamental principles, such as the maximum path entropy -- also known as Maximum Caliber principle -- , this work proposes an alternative derivation of the well-known Jarzynski equality, a nonequilibrium identity of great importance today due to its applications to irreversible processes: biological systems (protein folding), mechanical systems, among others. This equality relates the free energy differences between two equilibrium thermodynamic states with the work performed when going between those states, through an average over a path ensemble. In this work the analysis of Jarzynski's equality will be performed using the formalism of inference over path space. This derivation highlights the wide generality of Jarzynski's original result, which could even be used in non-thermodynamical settings such as social systems, financial and ecological systems.

cond-mat.stat-mech↗

arXiv2016

Plebanski-like action for general relativity and anti-self-dual gravity

We present a new $BF$-type action for complex general relativity with or without a cosmological constant resembling Plebanski's action, which depends on an SO(3,$\mathbb{C}$) connection, a set of 2-forms, a symmetric matrix, and a 4-form. However, it differs from the Plebanski formulation in the way that the symmetric matrix enters into the action. The advantage of this fact is twofold. First, as compared to Plebanski's action, the symmetric matrix can now be integrated out, which leads to a pure $BF$-type action principle for general relativity; the canonical analysis of the new action then shows that it has the same phase space of the Ashtekar formalism up to a canonical transformation induced by a topological term. Second, a particular choice of the parameters involved in the formulation produces a $BF$-type action principle describing conformally anti-self-dual gravity. Therefore, the new action unifies both general relativity and anti-self-dual gravity.

gr-qc↗

arXiv2016

Continuity equation for probability as a requirement of inference over paths

In this work we present the fundamental ideas of inference over paths, and show how this formalism implies the continuity equation, which is central for the derivation of the main partial differential equations that constitute non-equilibrium statistical mechanics. Equations such as the Liouville equation, Fokker-Planck equation, among others can be recovered as particular cases of the continuity equation, under different probability fluxes. We derive the continuity equation in its most general form through what we call the \bf time-slicing equation, which lays down the procedure to go from the representation in terms of a path probability functional $ρ[X()]$ to a time-dependent probability density $ρ(x; t)$. The original probability functional $ρ[X()]$ can in principle be constructed from different methods of inference; in this work we sketch an application using the maximum path entropy or maximum caliber principle.

cond-mat.stat-mech↗

arXiv2016

Liouville's Theorem from the Principle of Maximum Caliber in Phase Space

One of the cornerstones in non--equilibrium statistical mechanics (NESM) is Liouville's theorem, a differential equation for the phase space probability $ρ(q,p; t)$. This is usually derived considering the flow in or out of a given surface for a physical system (composed of atoms), via more or less heuristic arguments. In this work, we derive the Liouville equation as the partial differential equation governing the dynamics of the time-dependent probability $ρ(q, p; t)$ of finding a "particle" with Lagrangian $L(q, \dot{q}; t)$ in a specific point $(q, p)$ in phase space at time $t$, with $p=\partial L/\partial \dot{q}$. This derivation depends only on considerations of inference over a space of continuous paths. Because of its generality, our result is valid not only for "physical" systems but for any model depending on constrained information about position and velocity, such as time series.

physics.class-ph↗

arXiv2015

Hamiltonian formalism and path entropy maximization

Maximization of the path information entropy is a clear prescription for constructing models in non-equilibrium statistical mechanics. Here it is shown that, following this prescription under the assumption of arbitrary instantaneous constraints on position and velocity, a Lagrangian emerges which determines the most probable trajectory. Deviations from the probability maximum can be consistently described as slices in time by a Hamiltonian, according to a nonlinear Langevin equation and its associated Fokker-Planck equation. The connections unveiled between the maximization of path entropy and the Langevin/Fokker-Planck equations imply that missing information about the phase space coordinate never decreases in time, a purely information-theoretical version of the Second Law of Thermodynamics. All of these results are independent of any physical assumptions, and thus valid for any generalized coordinate as a function of time, or any other parameter. This reinforces the view that the Second Law is a fundamental property of plausible inference.

physics.data-an↗

arXiv2015

Gauge connection formulations for general relativity

We report a new class of $SO(3,\mathbb{C})$ and diffeomorphism invariant formulations for general relativity with either a vanishing or a nonvanishing cosmological constant, which depends functionally on a $SO(3,\mathbb{C})$ gauge connection and a complex-valued 4-form via a holomorphic function of the trace of a symmetric $3\times3$ matrix that is constructed from these variables. We present two members of this class, one of which results from the implementation of a method for obtaining action principles belonging to the class. For the case of a nonvanishing cosmological constant, we solve for the complex-valued 4-form and get pure connection action principles. We perform the canonical analysis of the class. The analysis shows that only the Hamiltonian constraint is modified with respect to the Ashtekar formulation and that the members of the class have two physical degrees of freedom per space point.

gr-qc↗

arXiv2014

A Bayesian interpretation of abrupt phase transitions

The formalism used in describing the thermodynamics of abrupt (or first-order) phase transitions is reviewed as an application of maximum entropy inference. In this treatment, we show that the concepts of transition temperature, latent heat and entropy difference between phases will inevitably have an equivalent in any problem of inferring the result of a yes/no question, given information in the form of expectation values.

cond-mat.stat-mech↗

arXiv2014

Fitting of interatomic potentials without forces: a parallel particle swarm optimization algorithm

We present a methodology for fitting interatomic potentials to ab initio data, using the particle swarm optimization (PSO) algorithm, needing only a set of positions and energies as input. The prediction error of energies associated with the fitted parameters can be close to 1 meV/atom or lower, for reference energies having a standard deviation of about 0.5 eV/atom. We tested our method by fitting a Sutton-Chen potential for copper from \emph{ab initio} data, which is able to recover structural and dynamical properties, and obtain a better agreement of the predicted melting point versus the experimental value, as compared to the prediction of the standard Sutton-Chen parameters.

cond-mat.mtrl-sci↗

arXiv2013

Newtonian Dynamics from the principle of Maximum Caliber

The foundations of Statistical Mechanics can be recovered almost in their entirety from the Principle of Maximum Entropy. In this work we show that its non-equilibrium generalization, the Principle of Maximum Caliber (Jaynes, 1980), when applied to the unknown trajectory followed by a particle, leads to Newton's second law under two quite intuitive assumptions (the expected square displacement in one step and the spatial probability distribution of the particle are known at all times). Our derivation explicitly highlights the role of mass as an emergent measure of the fluctuations in velocity (inertia) and the origin of potential energy as a manifestation of spatial correlations. According to our findings, the application of Newton's equations is not limited to mechanical systems, and therefore could be used in modelling ecological, financial and biological systems, among others.

physics.data-an↗