Machine-Proof of Entropy Inequalities

2021 ◽  
pp. 1-1
Author(s):  
Raymond W Yeung ◽  
Cheuk Ting Li
Keyword(s):  
Entropy Inequalities

scholarly journals RELAXATION OF FLUID SYSTEMS

2012 ◽  
Vol 22 (08) ◽  
pp. 1250014 ◽  
Author(s):  
FRÉDÉRIC COQUEL ◽  
EDWIGE GODLEWSKI ◽  
NICOLAS SEGUIN
Keyword(s):  
Numerical Method ◽  
Weak Solutions ◽  
Equilibrium Model ◽  
Numerical Approximation ◽  
Natural Extension ◽  
Fluid Models ◽  
Relaxation System ◽  
Fluid Systems ◽  
Relaxation Procedure ◽  
Entropy Inequalities

We propose a relaxation framework for general fluid models which can be understood as a natural extension of the Suliciu approach in the Euler setting. In particular, the relaxation system may be totally degenerate. Several stability properties are proved. The relaxation procedure is shown to be efficient in the numerical approximation of the entropy weak solutions of the original PDEs. The numerical method is particularly simple in the case of a fully degenerate relaxation system for which the solution of the Riemann problem is explicit. Indeed, the Godunov solver for the homogeneous relaxation system results in an HLLC-type solver for the equilibrium model. Discrete entropy inequalities are established under a natural Gibbs principle.

Quantum α-entropy inequalities: independent condition for local realism?

1996 ◽  
Vol 210 (6) ◽  
pp. 377-381 ◽  
Author(s):  
R. Horodecki ◽  
P. Horodecki ◽  
M. Horodecki
Keyword(s):  
Local Realism ◽  
Independent Condition ◽  
Entropy Inequalities

scholarly journals Entropy inequalities for unbounded spin systems

2002 ◽  
Vol 30 (4) ◽  
pp. 1959-1976 ◽  
Author(s):  
Paolo Dai Pra ◽  
Anna Maria Paganoni ◽  
Gustavo Posta
Keyword(s):  
Spin Systems ◽  
Unbounded Spin Systems ◽  
Entropy Inequalities ◽  
Unbounded Spin

scholarly journals On numerical entropy inequalities for a class of relaxed schemes

2001 ◽  
Vol 59 (2) ◽  
pp. 391-399 ◽  
Author(s):  
Huazhong Tang ◽  
Tao Tang ◽  
Jinghua Wang
Keyword(s):  
Entropy Inequalities ◽  
Numerical Entropy

scholarly journals Non-commutative Calculus, Optimal Transport and Functional Inequalities in Dissipative Quantum Systems

2019 ◽  
Vol 178 (2) ◽  
pp. 319-378 ◽  
Author(s):  
Eric A. Carlen ◽  
Jan Maas
Keyword(s):  
Spectral Gap ◽  
Optimal Transport ◽  
Quantum Systems ◽  
Sobolev Inequalities ◽  
Unified Framework ◽  
Logarithmic Sobolev Inequalities ◽  
Curvature Bounds ◽  
Finite Dimensional ◽  
Dissipative Quantum Systems ◽  
Entropy Inequalities

AbstractWe study dynamical optimal transport metrics between density matrices associated to symmetric Dirichlet forms on finite-dimensional $$C^*$$ C ∗ -algebras. Our setting covers arbitrary skew-derivations and it provides a unified framework that simultaneously generalizes recently constructed transport metrics for Markov chains, Lindblad equations, and the Fermi Ornstein–Uhlenbeck semigroup. We develop a non-nommutative differential calculus that allows us to obtain non-commutative Ricci curvature bounds, logarithmic Sobolev inequalities, transport-entropy inequalities, and spectral gap estimates.

scholarly journals Improvement of the Hydrostatic Reconstruction Scheme to Get Fully Discrete Entropy Inequalities

2019 ◽  
Vol 80 (2) ◽  
pp. 924-956
Author(s):  
Christophe Berthon ◽  
Arnaud Duran ◽  
Françoise Foucher ◽  
Khaled Saleh ◽  
Jean De Dieu Zabsonré
Keyword(s):  
Fully Discrete ◽  
Reconstruction Scheme ◽  
Entropy Inequalities

scholarly journals A MUSCL method satisfying all the numerical entropy inequalities

1996 ◽  
Vol 65 (216) ◽  
pp. 1439-1462 ◽  
Author(s):  
F. Bouchut ◽  
Ch. Bourdarias ◽  
B. Perthame
Keyword(s):  
Entropy Inequalities ◽  
Numerical Entropy
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