相关论文: Convex Entropy Decay via the Bochner-Bakry-Emery a…
We investigate the performance of entropy estimation methods, based either on block entropies or compression approaches, in the case of bidimensional sequences. We introduce a validation dataset made of images produced by a large number of…
The entropy of a binary symmetric Hidden Markov Process is calculated as an expansion in the noise parameter epsilon. We map the problem onto a one-dimensional Ising model in a large field of random signs and calculate the expansion…
The convergence to equilibrium for renormalised solutions to nonlinear reaction-diffusion systems is studied. The considered reaction-diffusion systems arise from chemical reaction networks with mass action kinetics and satisfy the complex…
Entropy estimation is a fundamental problem in information theory that has applications in various fields, including physics, biology, and computer science. Estimating the entropy of discrete sequences can be challenging due to limited data…
We establish the equivalence between exponential decay of the relative entropy along a quantum Markov semigroup and the modified logarithmic Sobolev inequality for general von Neumann algebras. We also extend an intertwining criterion for…
The quantitative convergence to equilibrium for reaction-diffusion systems arising from complex balanced chemical reaction networks with mass action kinetics is studied by using the so-called entropy method. In the first part of the paper,…
We consider the problem of energy decay rates for nonlinearly damped abstract infinite dimensional systems. We prove sharp, simple and quasi-optimal energy decay rates through an indirect method, namely a weak observability estimate for the…
By using the Jacobi metric of the configuration space, and assuming ergodicity, we calculate the Boltzmann entropy $S$ of a finite-dimensional system around a non-degenerate critical point of its potential energy $V$. We compare $S$ with…
Let $K = \{0,1,...,q-1\}$. We use a special class of translation invariant measures on $K^\mathbb{Z}$ called algebraic measures to study the entropy rate of a hidden Markov processes. Under some irreducibility assumptions of the Markov…
In this paper we study the effect of randomness on a linearized BGK-model in one dimension. We prove exponential decay rate to a global equilibrium. This decay rate can be proven to be independent of the stochastic influence in a physical…
Typically, the entropy of an isolated system in equilibrium is calculated by counting the number of accessible microstates, or in more general cases by using the Gibbs formula. In irreversible processes entropy spontaneously increases and…
We study hypocoercivity for a class of linearized BGK models for continuous phase spaces. We develop methods for constructing entropy functionals that enable us to prove exponential relaxation to equilibrium with explicit and physically…
Many classification models produce a probability distribution as the outcome of a prediction. This information is generally compressed down to the single class with the highest associated probability. In this paper, we argue that part of…
We develop the method of Maximum Entropy (ME) as a technique to generate approximations to probability distributions. The central results consist in (a) justifying the use of relative entropy as the uniquely natural criterion to select a…
We describe five types of results concerning information and concentration of discrete random variables, and relationships between them, motivated by their counterparts in the continuous case. The results we consider are information…
Continuous-time Markov chains associated to finite-volume discretization schemes of Fokker-Planck equations are constructed. Sufficient conditions under which quantitative exponential decay in the $\phi$-entropy and Wasserstein distance are…
The entropy production rate of nonequilibrium systems is studied via the Fokker-Planck equation. This approach, based on the entropy production rate equation given by Schnakenberg from a master equation, requires information of the…
There is a relation between the irreversibility of thermodynamic processes as expressed by the breaking of time-reversal symmetry, and the entropy production in such processes. We explain on an elementary mathematical level the relations…
Maximum entropy method for analytic continuation is extended by introducing quantum relative entropy. This new method is formulated in terms of matrix-valued functions and therefore invariant under arbitrary unitary transformation of input…
A quantity of interest to characterise continuous-valued stochastic processes is the differential entropy rate. The rate of convergence of many properties of LRD processes is slower than might be expected, based on the intuition for…