Related papers: Waiting-time based entropy estimators in continuou…
We study the motion of a particle in a random time-dependent vector field defined by the 2D Navier-Stokes system with a noise. Under suitable non-degeneracy hypotheses we prove that the empirical measures of the trajectories of the pair…
Entropy is a fundamental concept from Thermodynamics and it can be used to study models on context of Creation Cold Dark Matter (CCDM). From conditions on the first ($\dot{S}\geq0$)\footnote{Throughout the present work we will use dots to…
This paper considers a simulation-based estimator for a general class of Markovian processes and explores some strong consistency properties of the estimator. The estimation problem is defined over a continuum of invariant distributions…
One among the most intriguing results coming from the application of statistical mechanics to the study of brain is the understanding that it, as a dynamical system, is inherently out of equilibrium. In the realm of non-equilibrium…
Autoregressive generative models -- including Transformers, recurrent neural networks, classical Kalman filters, state space models, and Mamba -- all generate sequences by sampling each output from a deterministic summary of the past,…
We prove that the transport of any differentiable scalar observable in $d$-dimensional non-equilibrium systems is bounded from above by the total entropy production scaled by the amount the observation "stretches" microscopic coordinates.…
Energy flow in bio-molecular motors and machines are vital to their function. Yet experimental observations are often limited to a small subset of variables that participate in energy transport and dissipation. Here we show, through a…
We consider overdamped physical systems evolving under a feedback-controlled fluctuating potential and in contact with a thermal bath at temperature $T$. A Markovian description of the dynamics, which keeps only the last value of the…
In a particle physics dynamics, we assume a uniform distribution as the physical measure and a measure-theoretic definition of entropy on the velocity configuration space. This distribution is labeled as the physical solution in the…
This work is devoted to the investigation of the most probable transition time between metastable states for stochastic dynamical systems. Such a system is modeled by a stochastic differential equation with non-vanishing Brownian noise, and…
We derive a variational expression for the correlation time of physical observables in steady-state diffusive systems. As a consequence of this variational expression, we obtain lower bounds on the correlation time, which provide speed…
Fluctuation theorems are key to understanding both fundamental and applied aspects of non-equilibrium thermodynamics of small systems. We study the non-Markovian entropy production fluctuation theorem for the diffusion process of charged…
The ordinal approach to evaluate time series due to innovative works of Bandt and Pompe has increasingly established itself among other techniques of nonlinear time series analysis. In this paper, we summarize and generalize the theory of…
The entropy production rate is a key quantity in non-equilibrium thermodynamics of both classical and quantum processes. No universal theory of entropy production is available to date, which hinders progress towards its full grasping. By…
We study entropy production (EP) in processes involving repeated quantum measurements of finite quantum systems. Adopting a dynamical system approach, we develop a thermodynamic formalism for the EP and study fine aspects of irreversibility…
The paper studies asymptotic properties of estimators of multidimensional stochastic differential equations driven by Brownian motions from high-frequency discrete data. Consistency and central limit properties of a class of estimators of…
Topological entropy serves as a viable candidate for quantifying mixing and complexity of a highly chaotic system. Particularly in turbulence, this is determined as the exponential stretching rate of a fluid material line that typically…
We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may…
We formulate a stochastic description of entropy production in scattering theory for coherent transport. We distinguish between the information entropy change due to partial knowledge of the leads' state and the thermodynamic entropy change…
The rate of change of entropy $\dot S$ is measured for a system of particles floating on the surface of a fluid maintained in a turbulent steady state. The resulting coagulation of the floaters allows one to relate $\dot S$ to the velocity…