Related papers: Stability estimates for systems of nonlocal balanc…
We investigate the memory properties of discrete sequences built upon a finite number of states. We find that the block entropy can reliably determine the memory for systems modeled as Markov chains of arbitrary finite order. Further, we…
For a class of systems of nonlinear and nonlocal balance laws in several space dimensions, we prove the local in time existence of solutions and their continuous dependence on the initial datum. The choice of this class is motivated by a…
The historical process of the genesis of the extensive or substance-like quantities took place in two steps. First, global conservation or non-conservation was discovered. Only later did it become possible to formulate the balance locally…
We investigate and clarify the notion of locality as it pertains to the cascades of two-dimensional turbulence. The mathematical framework underlying our analysis is the infinite system of balance equations that govern the generalized…
Non-equilibrium systems have long-ranged spatial correlations even far away from critical points. This implies that the likelihoods of spatial steady state profiles of physical observables are nonlocal functionals. In this letter, it is…
We find the relation between reliability and entropy production in a realistic model of electronic memory (low-power MOS-based SRAM) where logical values are encoded as metastable non-equilibrium states. We employ large deviations…
Exploiting previous results on Markovian dynamics and fluctuation theorems, we study the consequences of memory effects on single realizations of nonequilibrium processes within an open system approach. The entropy production along single…
We study a nonlocal balance equation that describes the evolution of a system consisting of infinitely many identical particles those move along a deterministic dynamics and can also either disappear or give a spring. In this case, the…
Stable numerical simulations for a hyperbolic system of conservation laws of relaxation type but not in divergence form are obtained by incorporating the physical entropy into the simulations. The entropy balance is utilized as an…
Quantitative estimates are derived, on the whole space, for the relative entropy between the joint law of random interacting particles and the tensorized law at the limiting systeme. The developed method combines the relative entropy method…
In this paper, the long-time asymptotic behaviours of nonlocal porous medium equations with absorption or convection are studied. In the parameter regimes when the nonlocal diffusion is dominant, the entropy method is adapted in this…
We report the results of a numerical study of nonequilibrium steady states for a class of Hamiltonian models. In these models of coupled matter-energy transport, particles exchange energy through collisions with pinned-down rotating disks.…
We address the approximation of entropy solutions to initial-boundary value problems for nonlinear strictly hyperbolic conservation laws using neural networks. A general and systematic framework is introduced for the design of efficient and…
We prove that adapted entropy solutions of scalar conservation laws with discontinuous flux are stable with respect to changes in the flux under the assumption that the flux is strictly monotone in u and the spatial dependency is piecewise…
The steady state of a Langevin equation with short ranged memory and coloured noise is analyzed. When the fluctuation-dissipation theorem of second kind is not satisfied, the dynamics is irreversible, i.e. detailed balance is violated. We…
We study a 1D scalar conservation law whose non-local flux has a single spatial discontinuity. This model is intended to describe traffic flow on a road with rough conditions. We approximate the problem through an upwind-type numerical…
General hyperbolic systems of balance laws with inhomogeneous flux and source are studied. Global existence of entropy weak solutions to the Cauchy problem is established for small $BV$ data under appropriate assumptions on the decay of the…
We study the finite volume approximation of strong solutions to nonlinear systems of conservation laws. We focus on time-explicit schemes on unstructured meshes, with entropy satisfying numerical fluxes. The numerical entropy dissipation is…
This chapter deals with our recent attempt to extend the notion of equilibrium (EQ) entropy to nonequilibrium (NEQ) systems so that it can also capture memory effects. This is done by enlarging the equilibrium state space by introducing…
We consider the problem of existence of entropy weak solutions to scalar balance laws with a dissipative source term. The flux function may be discontinuous with respect both to the space variable x and the unknown quantity u. The problem…