Related papers: Gaussian time-translation covariant operations: st…
We consider some basic problems associated with quantum mechanics of systems having a time-dependent Hilbert space. We provide a consistent treatment of these systems and address the possibility of describing them in terms of a…
Using the recently proposed covariant framework of general relativistic stochastic mechanics and stochastic thermodynamics, we proved the detailed and integral fluctuation theorems in curved spacetime. The time-reversal transformation is…
Time directions are not invariant in conventional thermodynamics. We broadly follow ideas of Ludwig Boltzmann and investigate implications of postulating time-directional invariance in thermodynamics. In this investigation, we require that…
Our fundamental theories, i.e., the quantum theory and general relativity, are invariant under time reversal. Only when we treat system from the point of view of thermodynamics, i.e., averaging between many subsystem components, an arrow of…
Spatio-temporal covariances are important for describing the spatio-temporal variability of underlying random processes in geostatistical data. For second-order stationary processes, there exist subclasses of covariance functions that…
Quantum walks function as essential means to implement quantum simulators, allowing one to study complex and often directly inaccessible quantum processes in controllable systems. In this contribution, the notion of a driven Gaussian…
Gaussian processes are arguably the most important class of spatiotemporal models within machine learning. They encode prior information about the modeled function and can be used for exact or approximate Bayesian learning. In many…
In this short review article, we present recent progress in quantum thermodynamics in the framework with a correlated catalyst. We examine two key properties of thermal operations, the Gibbs preserving property and the covariant property.…
In data science, one is often confronted with a time series representing measurements of some quantity of interest. Usually, as a first step, features of the time series need to be extracted. These are numerical quantities that aim to…
We develop a mathematical framework for quantum time transfer based on commuting families of Hamiltonians and synchronization observables. The synchronization subspace is defined as the kernel of a difference operator between local clocks,…
In quantum mechanics, time is introduced as a non-measurable quantity, as there is no possibility to build a hermitian operator canonically conjugated to the Hamiltonian. We cannot have, therefore, the time operator, which means that the…
In thermodynamics, quantum coherences - superpositions between energy eigenstates - behave in distinctly nonclassical ways. Recently mathematical frameworks have emerged to account for these features and have provided a range of novel…
Time crystals are quantum many-body systems which are able to self-organize their motion in a periodic way in time. Discrete time crystals have been experimentally demonstrated in spin systems. However, the first idea of spontaneous…
The comparison of form factors calculated from a single-particle current in different relativistic quantum mechanic approaches evidences tremendous discrepancies. The role of constraints coming from space-time translations is considered…
Credible forecasting and representation learning of dynamical systems are of ever-increasing importance for reliable decision-making. To that end, we propose a family of Gaussian processes (GP) for dynamical systems with linear…
A general-covariant statistical framework capable of describing classical fluctuations of the gravitational field is a thorny open problem in theoretical physics, yet ultimately necessary to understand the nature of the gravitational…
Data assimilation in models representing spatio-temporal phenomena poses a challenge, particularly if the spatial histogram of the variable appears with multiple modes. The traditional Kalman model is based on a Gaussian initial…
Nonlinear dynamical systems are ubiquitous in science and engineering, yet analysis and prediction of these systems remains a challenge. Koopman operator theory circumvents some of these issues by considering the dynamics in the space of…
The observable outputs of many complex dynamical systems consist in time series exhibiting autocorrelation functions of great diversity of behaviors, including long-range power-law autocorrelation functions, as a signature of interactions…
Continuous-variable quantum thermodynamics in the Gaussian regime provides a promising framework for investigating the energetic role of quantum correlations, particularly in optical systems. In this work, we introduce an entropy-free…