Related papers: Maximal dissipation principle for the complete Eul…
The principle of maximum entropy provides a useful method for inferring statistical mechanics models from observations in correlated systems, and is widely used in a variety of fields where accurate data are available. While the assumptions…
In this work, the space of admissible entropy functions for the compressible multicomponent Euler equations is explored, following up on [Harten, \textit{J. Comput. Phys.}, 49 (1), 1983, pp. 151-164]. This effort allows us to prove a…
We are concerned with the global existence of entropy solutions for the compressible Euler equations describing the gas flow in a nozzle with general cross-sectional area, for both isentropic and isothermal fluids. New viscosities are…
We first construct the global unique solution by assuming that the initial data is small in the $H^3$ norm but the higher order derivatives could be large. If further the initial data belongs to $\Dot{H}^{-s}$ ($0\le s<3/2$) or…
We study on the whole space R d the compressible Euler system with damping coupled to the Poisson equation when the damping coefficient tends towards infinity. We first prove a result of global existence for the Euler-Poisson system in the…
We propose a method for transforming probability distributions so that parameters of interest are forced into a specified distribution. We prove that this approach is the maximum entropy choice, and provide a motivating example applicable…
We propose an approach to the realization of many-body quantum state distributions inspired by combined principles of thermodynamics and mesoscopic physics. Its essence is a maximum entropy principle conditioned by conservation laws. We go…
After the justification of the maximum entropy approach for equilibrium thermodynamic system, and of a maximum path entropy algorithm for nonequilibrium thermodynamic systems by virtue of the principle of virtual work, we present in this…
In this paper, we consider the stochastic optimal control problem for the interacting particle system. We obtain the stochastic maximum principle of the optimal control system by introducing a generalized backward stochastic differential…
According to the Narnhofer Thirring Theorem interacting systems at finite temperature cannot be described by particles with a sharp dispersion law. It is therefore mandatory to develop new methods to extract particle masses at finite…
We introduce a novel concept of dissipative measure-valued martingale solution to the stochastic Euler equations describing the motion of an inviscid incompressible fluid. These solutions are characterized by a parametrized Young measure…
In classical thermodynamics the Euler relation is an expression for the internal energy as a sum of the products of canonical pairs of extensive and intensive variables. For quantum systems the situation is more intricate, since one has to…
In this paper we introduce three notions of measure theoretical entropy of a measurable cover U in a measure theoretical dynamical system. Two of them were already introduced in [R] and the new one is defined only in the ergodic case. We…
We investigate maximal potential energy dissipation as a selection criterion for subsolutions (coarse grained solutions) in the setting of the unstable Muskat problem. We show that both, imposing this criterion on the level of convex…
This study proposes a novel spatial discretization procedure for the compressible Euler equations that guarantees entropy conservation at a discrete level for thermally perfect gases. The procedure is based on a locally conservative…
Far-from-equilibrium thermodynamics underpins the emergence of life, but how has been a long-outstanding puzzle. Best candidate theories based on the maximum entropy production principle could not be unequivocally proven, in part due to…
We show how to determine the maximum and minimum possible values of one measure of entropy for a given value of another measure of entropy. These maximum and minimum values are obtained for two standard forms of probability distribution (or…
We describe a maximum entropy approach for computing volumes and counting integer points in polyhedra. To estimate the number of points from a particular set X in R^n in a polyhedron P in R^n, by solving a certain entropy maximization…
In the paper, we introduce the maximum entropy estimator based on 2-dimensional empirical distribution of the observation sequence of hidden Markov model , when the sample size is big: in that case computing the maximum likelihood estimator…
In this article a classification of some proposed macroscopic entropy production (MEP) principles is given. With the help of simple electrical network models, at least six interesting and most used principles are distinguished: the least…