Entropy functions for symmetric systems of conservation laws
It is shown that symmetric systems of conservation laws are equipped with a one-parameter family of entropy functions. A simple symmetrizability criterion is used.
Tadmor, E.↗
SEARCH · Search NASA
Results for “entropy functional”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
A kinetic equation with kinetic entropy functions for scalar conservation laws
A nonlinear kinetic equation is constructed and proved to be well-adapted to describe general multidimensional scalar conservation laws. In particular, it is proved to be well-posed uniformly in epsilon - the microscopic scale. It is also shown that the proposed kinetic equation is equipped with a family of kinetic entropy functions - analogous to Boltzmann's microscopic H-function, such that they recover Krushkov-type entropy inequality on the macroscopic scale. Finally, it is proved by both - BV compactness arguments in the one-dimensional case, that the local density of kinetic particles admits a continuum limit, as it converges strongly with epsilon below 0 to the unique entropy solution of the corresponding conservation law.
Perthame, Benoit↗
The boundary entropy function for interface conformal field theories
In 1+1 dimensional conformal field theory with a boundary the boundary contribution to the entanglement entropy is determined by a single number g effectively counting the boundary degrees of freedom. In contrast, in 1+1 dimensional interface CFTs the corresponding quantity is a non-trivial function depending on the position of the interval relative to the interface, giving access to much more detailed information about the defect. In this work we determined this g -function in several examples using holography and derive some of its basic properties from holography and strong subadditivity.
AdS-CFT correspondence↗
Comments on Sen's classical entropy function for static and rotating AdS4 black holes
Not Available
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Entropy Pair Functional Theory: Direct Entropy Evaluation Spanning Phase Transitions
We prove that, within the class of pair potential Hamiltonians, the excess entropy is a universal, temperature-independent functional of the density and pair correlation function. This result extends Henderson’s theorem, which states that the free energy is a temperature dependent functional of the density and pair correlation. The stationarity and concavity of the excess entropy functional are discussed and related to the Gibbs–Bugoliubov inequality and to the free energy. We apply the Kirkwood approximation, which is commonly used for fluids, to both fluids and solids. Approximate excess entropy functionals are developed and compared to results from thermodynamic integration. The pair functional approach gives the absolute entropy and free energy based on simulation output at a single temperature without thermodynamic integration. We argue that a functional of the type, which is strictly applicable to pair potentials, is also suitable for first principles calculation of free energies from Born–Oppenheimer molecular dynamics performed at a single temperature. In conclusion, this advancement has the potential to reduce the evaluation the free energy to a simple modification to any procedure that evaluates the energy and the pair correlation function.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Empirical correlations between the function of entropy ( Z S ) and net artificial viscous work in a shock physics hydrocode
Entropy is a state variable that may be obtained from any thermodynamically complete equation of state (EOS). However, hydrocode calculations that output the entropy often contain numerical errors; this is not because of the EOS, but rather the solution techniques that are used in hydrocodes (especially Eulerian) such as convection, remapping, and artificial viscosity. Here, in this work, empirical correlations are investigated to reduce the errors in entropy without altering the solution techniques for the conservation of mass, momentum, and energy. Specifically, these correlations are developed for the function of entropy Z S , and they depend upon the net artificial viscous work, as determined via Sandia National Laboratories’ shock physics hydrocode CTH. These results are a continuation of a prior effort to implement the entropy-based CREST reactive burn model in CTH, and they are presented here to stimulate further interest from the shock physics community. Future work is planned to study higher-dimensional shock waves, shock wave interactions, and possible ties between the empirical correlations and a physical law.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Semi-discrete approximations to nonlinear systems of conservation laws; consistency and L(infinity)-stability imply convergence
A convergence theory for semi-discrete approximations to nonlinear systems of conservation laws is developed. It is shown, by a series of scalar counter-examples, that consistency with the conservation law alone does not guarantee convergence. Instead, a notion of consistency which takes into account both the conservation law and its augmenting entropy condition is introduced. In this context it is concluded that consistency and L(infinity)-stability guarantee for a relevant class of admissible entropy functions, that their entropy production rate belongs to a compact subset of H(loc)sup -1 (x,t). One can now use compensated compactness arguments in order to turn this conclusion into a convergence proof. The current state of the art for these arguments includes the scalar and a wide class of 2 x 2 systems of conservation laws. The general framework of the vanishing viscosity method is studied as an effective way to meet the consistency and L(infinity)-stability requirements. How this method is utilized to enforce consistency and stability for scalar conservation laws is shown. In this context we prove, under the appropriate assumptions, the convergence of finite difference approximations (e.g., the high resolution TVD and UNO methods), finite element approximations (e.g., the Streamline-Diffusion methods) and spectral and pseudospectral approximations (e.g., the Spectral Viscosity methods).
Tadmor, Eitan↗
Energy and maximum norm estimates for nonlinear conservation laws
We have devised a technique that makes it possible to obtain energy estimates for initial-boundary value problems for nonlinear conservation laws. The two major tools to achieve the energy estimates are a certain splitting of the flux vector derivative f(u)(sub x), and a structural hypothesis, referred to as a cone condition, on the flux vector f(u). These hypotheses are fulfilled for many equations that occur in practice, such as the Euler equations of gas dynamics. It should be noted that the energy estimates are obtained without any assumptions on the gradient of the solution u. The results extend to weak solutions that are obtained as point wise limits of vanishing viscosity solutions. As a byproduct we obtain explicit expressions for the entropy function and the entropy flux of symmetrizable systems of conservation laws. Under certain circumstances the proposed technique can be applied repeatedly so as to yield estimates in the maximum norm.
Olsson, Pelle↗
Augmented Adam-Gibbs model for glass melt viscosity and configuration entropy as functions of temperature and composition
As the temperature of glass melt increases, its structure approaches the state of a simple liquid while the configuration entropy approaches a maximum value. We describe this gradual change using a power law function of inverse temperature. The Adam-Gibbs model for glass viscosity as a function of temperature and glass composition augmented in this way is greatly simplified when applied to common glass families occupying moderate composition regions, such as float glass or nuclear waste glasses, on which properties can be approximated as linear functions of composition. The parsimonious model thus obtained is preferable for use in optimizing glass formulation and mathematical modeling of glass melting and forming. For multicomponent glasses with N viscosity-affecting components, the augmented Adam-Gibbs model requires 2N + 3 adjustable parameters. The model efficacy is demonstrated by fitting the model to a viscosity-temperature-composition dataset for low-activity nuclear waste glasses.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Entanglement between two disjoint universes
We use the replica method to compute the entanglement entropy of a universe without gravity entangled in a thermofield-double-like state with a disjoint gravitating universe. Including wormholes between replicas of the latter gives an entropy functional which includes an “island” on the gravitating universe. We solve the back-reaction equations when the cosmological constant is negative to show that this island coincides with a causal shadow region that is created by the entanglement in the gravitating geometry. At high entanglement temperatures, the island contribution to the entropy functional leads to a bound on entanglement entropy, analogous to the Page behavior of evaporating black holes. We demonstrate that the entanglement wedge of the non-gravitating universe grows with the entanglement temperature until, eventually, the gravitating universe can be entirely reconstructed from the non-gravitating one.
2D gravity↗
Wigner distribution function and entropy of the damped harmonic oscillator within the theory of the open quantum systems
The harmonic oscillator with dissipation is studied within the framework of the Lindblad theory for open quantum systems. By using the Wang-Uhlenbeck method, the Fokker-Planck equation, obtained from the master equation for the density operator, is solved for the Wigner distribution function, subject to either the Gaussian type or the delta-function type of initial conditions. The obtained Wigner functions are two-dimensional Gaussians with different widths. Then a closed expression for the density operator is extracted. The entropy of the system is subsequently calculated and its temporal behavior shows that this quantity relaxes to its equilibrium value.
Isar, Aurelian↗
Dual‐Functional High‐Entropy Polymer Exhibiting Giant Cross‐Energy Couplings at Low Fields
A key component of cooling devices is the transfer of entropy from the cold load to heat sink. An electrocaloric (EC) polymer capable of generating both large electrocaloric effect (ECE) and substantial electroactuation can enable EC cooling devices to pump heat without external mechanisms, resulting in compact designs and enhanced efficiency. However, achieving both high ECE and significant electroactuation remains challenging. Herein, it is demonstrated that poly(vinylidene fluoride‐trifluoroethylene‐chlorofluoroethylene‐double bond) [P(VDF‐TrFE‐CFE‐DB)] tetrapolymers can simultaneously generate high electrocaloric effects and electroactuations under low fields. These P(VDF‐TrFE‐CFE‐DB) tetrapolymers are synthesized through the dehydrochlorination of P(VDF‐TrFE‐CFE) terpolymer. By facile tuning the composition of the initial terpolymer to avoid pure relaxor state, tetrapolymers with optimal DB compositions are achieved, near the critical endpoint of normal ferroelectric phase with diffused phase transition. The nearly vanishing energy barriers between the nonpolar to polar phases result in a strong electrocaloric response and significant electroactuation. Specifically, the P(VDF‐TrFE‐CFE‐DB) tetrapolymer exhibits an EC entropy change Δ S of 100 J kg −1 K −1 under 100 MV m −1 : comparable to state‐of‐the‐art (SOA) EC polymers, while delivering nearly twice the electroactuation of the SOA EC polymers. This work presents a general strategy for developing EC materials that combine large electrocaloric effect and electroactuation at low electric fields.
36 MATERIALS SCIENCE↗
Empirical Correlations Between the Function of Entropy (Zs) and Net Artificial Viscous Work in a Shock Physics Hydrocode
Explore the source record for details and available documents.
Kittell, David E.↗
A new method for detecting abrupt changes in the dependence among multivariate hydrological series based on moving cut total correlation
Knowledge of how to define and estimate the dependence among multivariate hydrological series is essential for detecting abrupt changes in the dependence. Here, in this paper, a new method (BMCTC) is proposed to detect all possible abrupt change points in the dependence among multivariate hydrological series. The total correlation estimated by the matrix-based Renyi's alpha-order entropy functional is firstly introduced to define and measure the dependence strength among multivariate hydrological series. Then, the moving cut total correlation (MCTC) sequence is built by the moving window technique, which is used to measure changes in the dependence strength among multivariate hydrological series. Finally, the Bernaola-Galvan algorithm is used to detect all change points of the MCTC sequence. Simulations are performed to compare the effectiveness of BMCTC with Pearson correlation (BMCPC) and Spearman correlation (BMCSC), Cramer-von Mises (CvM) and copula-based likelihood-ratio (CLR). The results show that all change points are detected by BMCTC regardless of the samples size, but wrong change points or no change points are detected by other methods in most cases. BMCTC is applied to detect change points in the dependence among annual runoff, precipitation and sediment discharge series in the Xiliugou and the Kuyehe River, China. It is found that the dependence among runoff, precipitation and sediment discharge changed abruptly in 1980 and 1996 in the Kuyehe River and in 1999 in the Xiliugou River. These changes are mainly caused by human activities such as construction of water conservancy projects and coal mining.
54 ENVIRONMENTAL SCIENCES↗
Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. II. Entropy production and irreversibility of RG flows
Herein we demonstrate that the reformulation of renormalization group (RG) flow equations as nonlinear heat equations has severe implications on the understanding of RG flows in general. We demonstrate by explicitly constructing an entropy function for a zero-dimensional Z 2 -symmetric model that the dissipative character of generic nonlinear diffusion equations is also hard-coded in the functional RG equation. This renders RG flows manifestly irreversible, revealing the semigroup property of RG transformations on the level of the flow equation itself. Additionally, we argue that the dissipative character of RG flows, its irreversibility and the entropy production during the RG flow may be linked to the existence of a so-called C– / A-function. In total, this introduces an asymmetry in the so-called RG time—in complete analogy to the thermodynamic arrow of time—and allows for an interpretation of infrared actions as equilibrium solutions of dissipative RG flows equations. The impossibility of resolving microphysics from macrophysics is evident in this framework. Furthermore, we directly link the irreversibility and the entropy production in RG flows to an explicit numerical entropy production, which is manifest in diffusive and non-linear partial differential equations (PDEs) and a standard mathematical tool for the analysis of PDEs. Using exactly solvable zero-dimensional Z 2 -symmetric models, we explicitly compute the (numerical) entropy production related to the total variation nonincreasing property of the PDE during RG flows toward the infrared limit. Finally, we discuss generalizations of our findings and relations to the C– / A-theorem as well as how our work may help to construct truncations of RG flow equations in the future, including numerically stable schemes for solving the corresponding PDEs.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Data-driven, structure-preserving approximations to entropy-based moment closures for kinetic equations
In this study, we present a data-driven approach for approximating entropy-based closures of moment systems from kinetic equations. The proposed closure learns the entropy function by fitting the map between the moments and the entropy of the moment system, and thus does not depend on the spacetime discretization of the moment system or specific problem configurations such as initial and boundary conditions. With convex and C 2 approximations, this data-driven closure inherits several structural properties from entropy-based closures, such as entropy dissipation, hyperbolicity, and H-Theorem. We construct convex approximations to the Maxwell–Boltzmann entropy using convex splines and neural networks, test them on the plane source benchmark problem for linear transport in slab geometry, and compare the results to the standard, entropy-based systems which solve a convex optimization problem to find the closure. Numerical results indicate that these data-driven closures provide accurate solutions in much less computation time than that required by the optimization routine.
97 MATHEMATICS AND COMPUTING↗
Neural entropy-stable conservative flux form neural networks for learning hyperbolic conservation laws
We propose a neural entropy-stable conservative flux form neural network (NESCFN) for learning hyperbolic conservation laws and their associated entropy functions directly from solution trajectories, without requiring any predefined numerical discretization. While recent neural network architectures have successfully integrated classical numerical principles into learned models, most rely on prior knowledge of the governing equations or assume a fixed discretization. Our approach removes this dependency by embedding entropy-stable design principles into the learning process itself, enabling the discovery of physically consistent dynamics in a fully data-driven setting. By jointly learning both the flux function and a corresponding entropy, NESCFN promotes conservation and entropy dissipation, which is critical for long-term stability and fidelity in the system of hyperbolic conservation laws. Furthermore, numerical results demonstrate that the method achieves stability and conservation over extended time horizons and accurately captures shock propagation speeds, even without oracle access to future-time solution profiles in the training data.
Conservative flux form↗