Showing papers on "Entropy (classical thermodynamics) published in 1993"

Quantum Entropy and Its Use

Abstract: I Entropies for Finite Quantum Systems.- 1 Fundamental Concepts.- 2 Postulates for Entropy and Relative Entropy.- 3 Convex Trace Functions.- II Entropies for General Quantum Systems.- 4 Modular Theory and Auxiliaries.- 5 Relative Entropy of States of Operator Algebras.- 6 From Relative Entropy to Entropy.- 7 Functionals of Entropy Type.- III Channeling Transformation and Coarse Graining.- 8 Channels and Their Transpose.- 9 Sufficient Channels and Measurements.- 10 Dynamical Entropy.- 11 Stationary Processes.- IV Perturbation Theory.- 12 Perturbation of States.- 13 Variational Expression of Perturbational Limits.- V Miscellanea.- 14 Central Limit and Quasi-free Reduction.- 15 Thermodynamics of Quantum Spin Systems.- 16 Entropic Uncertainty Relations.- 17 Temperley-Lieb Algebras and Index.- 18 Optical Communication Processes.

Rational extended thermodynamics

Abstract: 1 Tour d'Horizon 2 Early Version of Extended Thermodynamics 1 Paradox of Heat Conduction and Shear Diffusion 1.1 Heuristic Derivation of the Laws of Fourier and Navier-Stokes 1.2 Parabolic Laws of Heat Conduction and Shear Diffusion 2 Paradox Removed 2.1 The Cattaneo Equation 2.2 Extended TIP 2.3 Finite Pulse Speeds in Extended TIP 2.4 Conclusion and Criticism 3 Kinetic Theory of Mon-atomic Gases 3.1 Boltzmann-Equation and Moments 3.2 Equations of Balance for Moments 3.3 Balance of Entropy and Possible Equilibria 3.4 The Grad Distribution 3.5 Entropy and Entropy Flux in Grad's 13-Moment Theory 3.6 Phenomenological Equations derived from the Kinetic Theory 3.7 Pulse Speeds 3.8 Conclusions 3 Formal Structure of Extended Thermodynamics 1 Field Equations 1.1 Thermodynamic Processes and Principles of the Constitutive Theory 1.2 Universal Principles of the Constitutive Theory 2 Entropy Inequality, Symmetric Hyperbolicity 2.1 Exploitation of the Entropy Inequality 2.2 Symmetric Hyperbolic Field Equations 2.3 Discussion 2.4 Characeristic Speeds 3 Main Subsystems 3.1 Constraints on the Main Field 3.2 A Main.

Thermodynamics in Geochemistry: The Equilibrium Model

Abstract: Introduction 1. Mathematical background 2. Thermodynamics terms 3. The first law of thermodynamics 4. The second law of thermodynamics 5. Statistical interpretation of entropy 6. Properties of simple systems 7. Applications to simple systems 8. Partial and apparent molar properties 9. Ideal solutions 10. Fugacity and activity 11. Standard states 12. The equilibrium constant 13. Heterogeneous and open systems 14. Solid solutions 15. Gaseous solutions 16. Aqueous electrolyte solutions 17. Redox systems 18. Speciation calculations

Physical properties of the half-filled Hubbard model in infinite dimensions.

Abstract: A detailed quantitative study of the physical properties of the infinite-dimensional Hubbard model at half filling is presented The method makes use of an exact mapping onto a single-impurity model supplemented by a self-consistency condition This coupled problem is solved numerically Results for thermodynamic quantities (specific heat, entropy, ), one-particle spectral properties, and magnetic properties (response to a uniform magnetic field) are presented and discussed The nature of the Mott-Hubbard metal-insulator transition found in this model is investigated A numerical solution of the mean-field equations inside the antiferromagnetic phase is also reported

Laser cooling of molecular internal degrees of freedom by a series of shaped pulses

Abstract: Laser cooling of the vibrational motion of a molecule is investigated. The scheme is demonstrated for cooling the vibrational motion on the ground electronic surface of HBr. The radiation drives the excess energy into the excited electronic surface serving as a heat sink. Thermodynamic analysis shows that this cooling mechanism is analogous to a synchronous heat pump where the radiation supplies the power required to extract the heat out of the system. In the demonstration the flow of energy and population from one surface to the other is analyzed and compared to the power consumption from the radiation field. The analysis of the flows shows that the phase of the radiation becomes the active control parameter which promotes the transfer of one quantity and stops the transfer of another. In the cooling process the transfer of energy is promoted simultaneously with the stopping population transfer. The cooling process is defined by the entropy reduction of the ensemble. An analysis based on the second law of thermodynamics shows that the entropy reduction on the ground surface is more than compensated for by the increase in the entropy in the excited surface. It is found that the rate of cooling reduces to zero when the state of the system approaches an energy eigenstate and is therefore a generalization of the third law of thermodynamics. The cooling process is modeled numerically for the HBr molecule by a direct solution of the Liouville von Neuman equation. The density operator is expanded using a Fourier basis. The propagation is done by a polynomial approximation of the evolution operator. A study of the influence of dissipation on the cooling process concludes that the loss of phase coherence between the ground and excited surface will stop the process.

Calculating maximum entropy flows in networks

Abstract: This paper describes methods for calculating the most likely values of link flows in networks with incomplete data. The object is to present a thorough and rigorous treatment of maximum entropy flow estimation methods and to develop a methodological framework capable of handling different types of network problems. A multiple probability space conditional entropy approach is described for the general network problem. Results are presented and discussed for an example network intended for water supply.

Information and entropy

Abstract: The Landauer cost for erasing information demands that information about a physical system be included in the total entropy, as proposed by Zurek [Nature 341, 119 (1989); Phys. Rev. A 40, 4731 (1989)]. A consequence is that most system states-either classical phase-space distributions or quantum pure states-have total entropy much larger than thermal equilibrium. If total entropy is to be a useful concept, this must imply that work can be extracted in going from equilibrium to a typical system state. The work comes from randomization of a «memory» that holds a record of the system state

Nonanalytic contributions to the self-energy and the thermodynamics of two-dimensional Fermi liquids

Abstract: We calculate the entropy of a two-dimensional Fermi liquid using a model with a contact interaction between fermions. We find that there are [ital T][sup 2] contributions to the entropy from interactions separate from those due to the collective modes. These [ital T][sup 2] contributions arise fron nonanalytic corrections to the real part of the self-energy which may be calculated from the leading-log dependence of the imaginary part of the self-energy through the Kramers-Kronig relation. We find no evidence of a breakdown in Fermi liquid theory in 2D and conclude that Fermi liquids in 2D are similar to 3D Fermi liquids.

Thermodynamics of Taylor dispersion: Constitutive equations.

Abstract: This paper shows that the Taylor dispersion flux is a dissipative flux of extended thermodynamics. Every term in the evolution equations for the Taylor flux components is connected to a thermodynamic function and the entropy production is proved to be positive definite. Thermodynamic restrictions on phenomenological coefficients are also satisfied.

Entropy production in the Au+Au reaction between 150A and 800A MeV

Abstract: HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Entropy production in the Au + Au reaction between 150 and 800 A MeV C. Kuhn, J. Konopka, J.P. Coffin, C. Cerruti, P. Fintz, G. Guillaume, A. Houari, F. Jundt, C. Maguire, F. Rami, et al.

The thermodynamical approach to the back reaction problem

Abstract: A new approach to the back reaction of Hawking radiation on a Schwarzschild black hole (SBH), based on thermodynamics, is proposed, in which the thermodynamical system composed of SBH and thermal radiation in curved space is treated as a thermodynamical system composed of SBH, thermal radiation and a two-dimensional thermodynamical membrane (i.e. event horizon) in flat space.

Rate type equations for the diffusion in polymers: Thermodynamic constraints

Abstract: Conditions imposed by the second law of thermodynamics on viscoelastic rate type constitutive equations for the diffusive mass flux are considered. The analysis of three different rate type models proposed in the literature points out that presently physically unrealistic predictions are possible in desorption processes. The thermodynamic analysis of such models, based on the entropy inequality and on the stability requirement of the equilibrium states, leads to precise relationships among relaxation times, diffusion coefficients, and entropy equations of state. In particular, the analysis shows that relaxation times and diffusion coefficients cannot be simply constant numbers. When the thermodynamic constraints imposed on the constitutive equations are introduced, the models do not show physically unrealistic behaviors any more; Fickian diffusion close to the pure penetrant or pure polymer regions is also recovered. Finally, it is shown that the stability requirement for the equilibrium states may introduce very rigid requirements for the model feasibility, well beyond what appears explicitly from the kinetic equations alone.

Thermodynamic functions for Taylor dispersion.

Abstract: The link between Taylor dispersion and irreversible thermodynamics pointed out by Camacho [Phys. Rev. E 47, 1049 (1993)] is substantiated through the study of the thermodynamic functions associated to Taylor dispersion. They are evaluated by two means. First, from the connection between the one-dimensional (1D) thermodynamic functions of extended thermodynamics---entropy, entropy flux, entropy production, and chemical potential---and the constitutive equations describing the dynamics of the Taylor flux components; and second, from a purely thermodynamic analysis in the three-dimensional (3D) space. Both independent procedures are shown to yield the same results, thus confirming the physical entity of the Taylor thermodynamic functions. The different interpretation of the same physical quantities given by 3D and 1D observers is thoroughly discussed.

NDE imaging of flaws using rapid computation of Shannon entropy

Abstract: Previous work has demonstrated the advantages of Shannon entropy (H) analysis for the image-based detection of defects in both plexiglas and graphite/epoxy composites [1][2][3]. Application to experimental data shows that the analysis is fast and robust in the presence of noise. However, it suffers from the shortcoming that when signal averaging is employed, H converges to a constant, independent of the underlying waveform characteristics (log2(Ns), where Ns is the number of gated time domain sample points). By considering a generalization of the Shannon entropy to the continuous waveform case, H c, we eliminate this problem and obtain a stable numerical scheme for evaluation of Hc based on the use of Fourier series. As described previously, however, this approach requires a network of 20 workstations over 20 hours to complete analysis of one 41 by 201 pixel image. We describe a new approach for calculating continuous waveform entropy Hc, based on the use of a Green's function. We show that the new approach produces the same or higher image contrast in a time that is roughly three orders of magnitude smaller than that required by the Fourier series method. This improvement arises from two sources. The Green's function approach has greater inherent immunity to noise, and requires fewer calculations than the Fourier series approach. The resulting algorithm makes it feasible to perform Hc analysis on a personal computer

Canonical formalism, fundamental equation, and generalized thermomechanics for irreversible fluids with heat transfer.

Abstract: A Lagrangian with dissipative (e.g., Onsager's) potentials is constructed for the field description of irreversible heat-conducting fluids, off local equilibrium. Extremum conditions of action yield Clebsch representations of temperature, chemical potential, velocities, and generalized momenta, including a thermal momentum introduced recently [R. L. Selinger and F. R. S. Whitham, Proc. R. Soc. London, Ser. A 302, 1 (1968); S. Sieniutycz and R. S. Berry, Phys. Rev. A 40, 348 (1989)]. The basic question asked is To what extent may irreversibility, represented by a given form of the entropy source, influence the analytical form of the conservation laws for the energy and momentum '' Noether's energy for a fluid with heat flow is obtained, which leads to a fundamental equation and extended Hamiltonian dynamics obeying the second law of thermodynamics. While in the case of the Onsager potentials this energy coincides numerically with the classical energy [ital E], it contains an extra term (vanishing along the path) still contributing to an irreversible evolution. Components of the energy-momentum tensor preserve all terms regarded standardly as irreversible'' (heat, tangential stresses, etc.) generalized to the case when thermodynamics includes the state gradients and the so-called thermal phase, which we introduce here. This variable, themore » Lagrange multiplier of the entropy generation balance, is crucial for consistent treatment of irreversible processes via an action formalism. We conclude with the hypothesis that embedding the first and second laws in the context of the extremal behavior of action under irreversible conditions may imply accretion of an additional term to the classical energy.« less

Thermodynamics of spray evaporation

Abstract: An exergy and anergy balance in the process of spray evaporation in hot gas surroundings has been made to determine the second law efficiency of the process. The law of entropy generation in droplet evaporation (from the authors' earlier work) has been taken as the fundamental information for evaluating the entropy generation rate due to evaporation of the dispersed phase in the spray. The entropy generation rate due to transport processes in the carrier phase has been evaluated from a two-phase separated flow model of the spray. A theoretical model for exergy analysis of the process of spray evaporation has been developed to predict the second law efficiency of the process in terms of pertinent controlling parameters like free stream temperature, initial Reynolds number and initial drop size distribution of the spray.

Computing unsteady shock waves for aeroacoustic applications

Abstract: The computation of unsteady shock waves, which contribute significantly to noise generation in supersonic jet flows, is investigated. This paper focuses on the difficulties of computing slowly moving shock waves. Numerical error is found to manifest itself principally as a spurious entropy wave. Calculations presented are performed using a third order essentially nonoscillatory scheme. The effect of stencil biasing parameters and of two versions of numerical flux formulas on the magnitude of spurious entropy are investigated. The level of numerical error introduced in the calculation in quantified as a function of shock pressure ratio, shock speed, Courant number, and mesh density. The spurious entropy relative to the entropy jump across a static shock decreases with increasing shock strength and shock velocity relative to the grid, but is insensitive to Courant number. The structure of the spurious entropy wave is affected by the choice of flux formulas and algorithm biasing parameters. The effect of the spurious numerical waves on the calculation of sound amplification by a shock wave is investigated. For this class of problem, the acoustic pressure waves are relatively unaffected by the spurious numerical phenomena.

Applications of Thermodynamics

Abstract: In Chap. 7, we attempted to explain the behavior and properties of macroscopic bodies with the assistance of our knowledge of microscopic interactions. We introduced terms such as entropy S, pressure p, temperature T and chemical potential μ. We called these quantities state variables and the set of state variables was structured by the Gibbs form $$ dE = TdS - pdV + \mu dN. $$ .

Non-equilibrium thermodynamics and dissipative fluid theories

Abstract: The first paper in this series investigated, from the mathematical point of view, several aspects of the thermodynamic fluid theories (of divergence type). The object of this second paper is to present a simple example of such a theory. Here the Grad moment method is applied to a classical Boltzmann equation to obtain a determined system of the quasi-linear, first-order partial differential equations for the evaluation of the usual hydrodynamic variables and the stress deviator. As demonstrated already by Loose and Hess (Phys. Rev. A,37, 2099 (1988)), these equations provide valuable information about the shear-rate dependence of the viscosity coefficients and on other non-Newtonian properties of the pressure tensor. Accidentally, for the above-mentioned choice of independent gas-state variables, the truncation scheme of Grad not only leads to a symmetric hyperbolic system of differential equations, but also is in complete agreement with the variational approach to Maxwell's equations of transfer. Thus the proposed method enables one to obtain the supplementary balance law, interpreted as the equation of balance of entropy, satisfied by a certain functionh of the original variables. This function,which in the present case can be calculated explicitly, is referred to as the specific entropy (per unit mass). The resulting non-linear expression forh is investigated with a view to a deeper understanding of a status of the extended Gibbs relation. Due to the existence of this relation, one easily arrives at the natural definitions of temperature, pressure, and thermodynamic potentials for gaseous systems «not infinitesimally near to equilibrium».

Dependence of phase transitions on small changes

Abstract: In this contribution, the generalized thermodynamic formalism is applied to a nonhyperbolic dynamical system in two comparable situations. The change from one situation to the other is small in the sense that the grammar and the singularities of the system are preserved. For the discussion of the effects generated by this change, the generalized entropy functions are calculated and the sets of the specific scaling functions which reflect the phase transition of the system are investigated. It is found that even under mild variations, this set is not invariant

Schaum's outline of theory and problems of thermodynamics for engineers

Abstract: Concepts, Definitions, and Basic Principles Properties of Pure Substances Work and Heat The First Law of Thermodynamics The Second Law of Thermodynamics Entropy Reversible Work, Irreversibility, and Availability Power and Refrigeration Vapor Cycles Power and Refrigeration Gas Cycles Thermodynamic Relations Mixtures and Solutions Combustion Appendixes: Conversion of Units Material Properties Thermodynamic Properties of Water (Steam Tables) Thermodynamic Properties of Freon 12 Thermodynamic Properties of Ammonia Ideal-Gas Tables o Psychrometric Charts Compressibility Chart Enthalpy Departure Charts Entropy Departure Charts Sample Screens from the Companion Schaum's Electronic Tutor A companion Schaum's Electronic Tutor is also available!

Riemannian structure of the thermodynamic phase space

Abstract: Following Weinhold's work, it is shown that it is possible to define a Riemannian metric on certain submanifolds of thc space of equilibrium states of a thermodynamic system and that Weinhold's abstract vector space can be identified with the tangent space to one of these submanifolds. 1t is also shown that the metric tensor can be wrillen in terms of second derivatives of the internal energy, of the entropy 01' of other thermodynamic potentials.