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This study explores information measures based on extropy, introducing dynamic relative extropy measures for residual and past lifetimes, and investigating their various properties. Furthermore, the study analyzes the relationships between…
This paper investigates the approximation of stochastic delay differential equations (SDDEs) via the backward Euler-Maruyama (BEM) method under generalized monotonicity and Khasminskii-type conditions in the infinite horizon. First, by…
An implicit Euler finite-volume scheme for general cross-diffusion systems with volume-filling constraints is proposed and analyzed. The diffusion matrix may be nonsymmetric and not positive semidefinite, but the diffusion system is assumed…
Consideration is given to the three different analytical methods for the computation of upper bounds for the rate of convergence to the limiting regime of one specific class of (in)homogeneous continuous-time Markov chains. This class is…
This paper aims to provide some tools coming from functional inequalities to deal with quasi-stationarity for absorbed Markov processes. First, it is shown how a Poincar\'e inequality related to a suitable Doob transform entails exponential…
Most high-dimensional estimation and prediction methods propose to minimize a cost function (empirical risk) that is written as a sum of losses associated to each data point. In this paper we focus on the case of non-convex losses, which is…
This short note presents the derivation of a new {\it a priori} estimate for the Oldroyd-B model. Such an estimate may provide useful information when investigating the long-time behaviour of macro-macro models, and the stability of…
Entropy production characterizes the thermodynamic irreversibility and reflects the amount of heat dissipated into the environment and free energy lost in nonequilibrium systems. According to the thermodynamic uncertainty relation, we…
We determine the minimal entropy martingale measure for a general class of stochastic volatility models where both price process and volatility process contain jump terms which are correlated. This generalizes previous studies which have…
We present here a general method based on the investigation of the relative energy of the system, that provides an unconditional error estimate for the approximate solution of the barotropic Navier Stokes equations obtained by time and…
This paper introduces entropy balancing for continuous treatments (EBCT) by extending the original entropy balancing methodology of Hainm\"uller (2012). In order to estimate balancing weights, the proposed approach solves a globally convex…
We consider systems of conservation laws endowed with a convex entropy. We show the contraction, up to a translation, to extremal entropic shocks, for a pseudo-distance based on the notion of relative entropy. The contraction holds for…
According to a previous conjecture, spatial and temporal Lyapunov exponents of chaotic extended systems can be obtained from derivatives of a suitable function: the entropy potential. The validity and the consequences of this hypothesis are…
The information detection of complex systems from data is currently undergoing a revolution, driven by the emergence of big data and machine learning methodology. Discovering governing equations and quantifying dynamical properties of…
We explore the use of the method of Maximum Entropy (ME) as a technique to generate approximations. In a first use of the ME method the "exact" canonical probability distribution of a fluid is approximated by that of a fluid of hard…
We introduce in this paper a new approach to the problem of the convergence to equilibrium for kinetic equations. The idea of the approach is to prove a 'weak' coercive estimate, which implies exponential or polynomial convergence rate. Our…
Entropy production is arguably the most universally applicable measure of non-equilibrium behavior, particularly for systems coupled to a heat bath. This setting encompasses driven soft matter as well as biomolecular, biochemical, and…
We present a method of estimating the rate of entropy production in underdamped dynamics by decomposing it into contributions originating in different non-equilibrium effects. Specifically, a non-zero average velocity, a non-thermal width…
A Bayesian nonparametric estimator to entropy is proposed. The derivation of the new estimator relies on using the Dirichlet process and adapting the well-known frequentist estimators of Vasicek (1976) and Ebrahimi, Pflughoeft and Soofi…
The study considers advantages of the introduced measure of time based on the entropy change under irreversible processes (entropy production). Using the example of non-equilibrium expansion of an ideal gas in vacuum, such a measure is…