Related papers: Diverging conditional correlation lengths in the a…
Multistate Markov models are a canonical parametric approach for data modeling of observed or latent stochastic processes supported on a finite state space. Continuous-time Markov processes describe data that are observed irregularly over…
In this article, addressing large $n$ systems, we report that in numerous systems hosting long and short range interactions, multiple correlation lengths may appear. The largest correlation lengths often monotonically increase with…
In the study of Markov chain mixing times, analysis has centered on the performance from a worst-case starting state. Here, in the context of Glauber dynamics for the one-dimensional Ising model, we show how new ideas from information…
An investigation of the performance of the multilevel algorithm in the approach to criticality has been undertaken using the Ising model, performing simulations across a range of temperatures. Numerical results show that the performance of…
We analyse dynamical large deviations of quantum trajectories in Markovian open quantum systems in their full generality. We derive a {\em quantum level-2.5 large deviation principle} for these systems, which describes the joint…
We investigate the thermalization of a stochastic system with discrete phase space, initially at equilibrium at temperature $T_i$ and then termalizing in an environment at temperature $T_f$ , considering both cases $T_i > T_f$ and $T_i <…
Lack of knowledge about the detailed many-particle motion on the microscopic scale is a key issue in any theoretical description of a macroscopic experiment. For systems at or close to thermal equilibrium, statistical mechanics provides a…
Extensive Monte Carlo simulations are employed in order to study the dynamic critical behavior of the one-dimensional Ising magnet, with algebraically decaying long-range interactions of the form $\frac{1}{r^{d+\sigma}}$, with…
Long-range quantum systems, in which the interactions decay as $1/r^{\alpha}$, are of increasing interest due to the variety of experimental set-ups in which they naturally appear. Motivated by this, we study fundamental properties of…
The classical Ising chain is the paradigm for the non-existence of phase transitions in 1D systems and was solved by Ernst Ising one hundred years ago. More recently, a decorated two leg Ising ladder has received interest for the curious…
The Markov property entails the conditional independence structure inherent in Gibbs distributions for general classical Hamiltonians, a feature that plays a crucial role in inference, mixing time analysis, and algorithm design. However,…
Information-theoretic quantities have received significant attention as system-independent measures of correlations in many-body quantum systems, e.g., as universal order parameters of synchronization. In this work, we present a method to…
Dynamic correlation and response functions of classical and quantum systems in thermal equilibrium are connected by fluctuation-dissipation theorems, which allow an alternative definition of their (unique) temperature. Motivated by this…
The quantum antiferromagnetic spin-1/2 Ising model on a triangular lattice and analogous fully frustrated Ising model on a square lattice with quantum fluctuations induced by the application of the transverse magnetic field are studied at…
We introduce quantum versions of the $\chi^2$-divergence, provide a detailed analysis of their properties, and apply them in the investigation of mixing times of quantum Markov processes. An approach similar to the one presented in [1-3]…
In this paper, we first introduce and define several new information divergences in the space of transition matrices of finite Markov chains which measure the discrepancy between two Markov chains. These divergences offer natural…
We consider an ordinary differential equation with a unique hyperbolic attractor at the origin, to which we add a small random perturbation. It is known that under general conditions, the solution of this stochastic differential equation…
What happens when one of the parameters governing the dynamics of a long-range interacting system of particles in thermal equilibrium is abruptly changed (quenched) to a different value? While a short-range system, under the same…
The capacity to integrate information is a prominent feature of biological and cognitive systems. Integrated Information Theory (IIT) provides a mathematical approach to quantify the level of integration in a system, yet its computational…
The existence of a static lengthscale that grows in accordance with the dramatic slowing down observed at the glass transition is a subject of intense interest. A recent publication compared two proposals for this length scale, one based on…