相关论文: Entropy Increasing Numerical Methods for Predictio…

Entropy is a central concept in physics, but can be challenging to calculate even for systems that are easily simulated. This is exacerbated out of equilibrium, where generally little is known about the distribution characterizing simulated…

This paper establishes the minimum entropy principle (MEP) for the relativistic Euler equations with a broad class of equations of state (EOSs) and addresses the challenge of preserving the local version of the discovered MEP in high-order…

The time decay of fully discrete finite-volume approximations of porous-medium and fast-diffusion equations with Neumann or periodic boundary conditions is proved in the entropy sense. The algebraic or exponential decay rates are computed…

This paper addresses the design of linear and nonlinear stabilization procedures for high-order continuous Galerkin (CG) finite element discretizations of scalar conservation laws. We prove that the standard CG method is entropy…

In this paper we design high-order positivity-preserving approximation schemes for an integro-differential model describing photochemical reactions. Specifically, we introduce and analyze three classes of dynamically consistent methods,…

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…

Trajectories provide dynamical information that is discarded in free energy calculations, for which we sought to design a scheme with the hope of saving cost for generating dynamical information. We first demonstrated that snapshots in 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…

We consider numerical methods for the Poisson-Nernst-Planck-Cahn-Hilliard (PNPCH) equations with steric interactions. We propose a novel energy stable numerical scheme that respects mass conservation and positivity at the discrete level.…

In this paper, the entropy conservative/stable algorithms presented by Del Rey Fernandez and coauthors [18,16,17] for the compressible Euler and Navier-Stokes equations on nonconforming p-refined/coarsened curvilinear grids is extended to…

The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible constrained to match empirical data, for instance, feature expectations. We seek to generalize…

High order schemes are known to be unstable in the presence of shock discontinuities or under-resolved solution features for nonlinear conservation laws. Entropy stable schemes address this instability by ensuring that physically relevant…

In this paper, we present first-order accurate numerical methods for solution of the heat equation with uncertain temperature-dependent thermal conductivity. Each algorithm yields a shared coefficient matrix for the ensemble set improving…

We compare two calculations of the particle density in the superfluid phase of the classical XY model with a chemical potential $\mu$ in 1+1 dimensions.The first relies on exact blocking formulas from the Tensor Renormalization Group (TRG)…

We extend the entropy stable high order nodal discontinuous Galerkin spectral element approximation for the non-linear two dimensional shallow water equations presented by Wintermeyer et al. [N. Wintermeyer, A. R. Winters, G. J. Gassner,…

Understanding nonequilibrium systems and the consequences of irreversibility for the system's behavior as compared to the equilibrium case, is a fundamental question in statistical physics. Here, we investigate two types of nonequilbrium…

This work analyzes different notions of entropy and its production in $ep$ and heavy-ion collisions, focusing on the early stages of the collision. To this end, the importance of phenomena such as quantum entanglement and decoherence in…

We translate the problem of calculating the entropy of a set of binary configurations/signals into a sequence of supervised classification tasks. Subsequently, one can use virtually any machine learning classification algorithm for…

Entropy is one of the key thermodynamic variables reflecting changes in the state of matter. Unlike other thermodynamic variables, it is well-defined also for nonequilibrium steady states through its relation to information. Applying this…

Entanglement entropy in topologically ordered matter phases has been computed extensively using various methods. In this paper, we study the entanglement entropy of topological phases in two-spaces from a new perspective---the perspective…