Related papers: Relative entropy in diffusive relaxation
In the framework of irreversible thermodynamics, we study autonomous systems of reaction-diffusion equations to show how the entropy and free energy of an open and irreversible reactor depend on concentrations. To do this, we find a…
We analyse convergence of a micro-macro acceleration method for the Monte Carlo simulation of stochastic differential equations with time-scale separation between the (fast) evolution of individual trajectories and the (slow) evolution of…
The aim of this study is to generalise recent results of the two last authors on en-tropy methods for measure solutions of the renewal equation to other classes of structured population problems. Specifically, we develop a generalised…
It is known that the viscosity of a dilute gas can be derived by using kinetic theory. We present here a new derivation by using two entropy production principles: the steepest entropy ascent (SEA) principle and the maximum entropy…
In his work about hypocercivity, Villani [18] considers in particular convergence to equilibrium for the kinetic Langevin process. While his convergence results in L 2 are given in a quite general setting, convergence in entropy requires…
We are concerned with the one-dimensional pressureless Euler system with relaxation in the Radon measure space. As the relaxation time tends to zero, the entropy solution converges to a static solution with the density converging to its…
A conditional entropic approach is discussed for nonequilibrium complex systems with a weak correlation between spatiotemporally fluctuating quantities on a large time scale. The weak correlation is found to constitute the fluctuation…
For general asymptotically sub-additive potentials (resp. asymptotically additive potentials) on general topological dynamical systems, we establish some variational relations between the topological entropy of the level sets of Lyapunov…
The relative entropy and chi-squared divergence are fundamental divergence measures in information theory and statistics. This paper is focused on a study of integral relations between the two divergences, the implications of these…
We consider the relative entropy between vacuum states of two different theories: a conformal field theory (CFT), and the CFT perturbed by a relevant operator. By restricting both states to the null Cauchy surface in the causal domain of a…
We are concerned with globally defined entropy solutions to the Euler equations for compressible fluid flows in transonic nozzles with general cross-sectional areas. Such nozzles include the de Laval nozzles and other more general nozzles…
Convex integration has revealed that the Euler system of gas dynamics is ill-posed in the class of weak solutions even if the entropy inequality is imposed as an additional constraint. A natural question arises, namely, if a physically…
We establish the existence and compactness of global martingale entropy solutions with finite relative-energy for the stochastically forced system of isentropic Euler equations governed by a general pressure law. To achieve these, a…
Although an intimate relation between entropy and diffusion has been advocated for many years and even seems to have been verified in theory and experiments, a quantitatively reliable study, and any derivation of an algebraic relation…
The time variation of entropy, as an alternative to the variance, is proposed as a measure of the diffusion rate. It is shown that for linear and time-translationally invariant systems having a large-time limit for the density, at large…
We study the long-time behavior of solutions to the compressible Euler equations with frictional damping in the whole space, where we prescribe direction-dependent values for the density at spatial infinity. To this end, we transform the…
In the context of control and estimation under information constraints, restoration entropy measures the minimal required data rate above which the state of a system can be estimated so that the estimation quality does not degrade over time…
The main objective of this paper is to prove that if capillarity effect is taken into account then there exist dissipative solutions to a system describing viscoplastic compressible flows with density dependent viscosities in a periodic…
A semi-implicit in time, entropy stable finite volume scheme for the compressible barotropic Euler system is designed and analyzed and its weak convergence to a dissipative measure-valued (DMV) solution [E. Feireisl et al., Dissipative…
Extending our previous work, we study the relative entropy between the reduced density matrices obtained from globally excited states in conformal field theories of arbitrary dimensions. We find a general formula in the small subsystem size…