Maximal Entropy Production Research Articles

Particle abundances and spectra in the hydrodynamical description of relativistic nuclear collisions with light projectiles

We show that a hydrodynamical model with continuous particle emission instead of sudden freeze-out may explain both the observed strange particle and pion abundances and transverse mass spectra for light projectiles at SPS energy. We found that the observed enhancement of pion production corresponds, within the context of continuous emission, to the maximal entropy production.

A Thermomechanical Modeling and Simulation of Viscoplastic Large Deformation Behavior for Polymeric Materials. 1st Report, Non-Coaxiality of Constitutive Equation Originated in Strain Rate Dependence.

Polymeric materials have various characteristics of deformation, e.g., strain rate dependence (viscoplasticity) at room temperature, strain localization just after initial yielding and propagation of a localized region with strain hardening. Viscoplasticity has been usually represented by a constitutive equation of plasticity with a hardening law including a plastic strain rate. However, such a modeling is not thermodynamically consistent with the hardening law dependent on strain rate. In this paper, a strain rate tensor is introduced into free energy and a thermodynamic force conjugate to this rate is newly defined. On the basis of the principle of increase of entropy and one of maximal entropy production rate, a non-coaxial constitutive equation of viscoplasticity is derived as a flow rule in which a dissipation function plays the role of plastic potential. It is shown that a strain rate dependent constitutive equation must be always non-coaxial in a thermodynamically consistent theory.

A Thermomechanical Modeling and Simulation of Viscoplastic Large Deformation Behavior for Polymeric Materials. 2nd Report, Vertex Model Based on Flow Rule and Its Finite Element Analysis.

In the previous paper, a strain rate tensor is introduced into free energy and a thermodynamic force conjugate to this rate is newly defined. On the basis of the principle of increase of entropy and one of maximal entropy production rate, a non-coaxial constitutive equation associated with a plastic deformation rate is derived as a flow rule in which a dissipation function plays the role of plastic potential. Material moduli in this equation, however, are still not expressed as functions of hardening law. In this paper, the constitutive equation is newly generalized into corner theory which permits an existence of a vertex on dissipation surface. A non-coaxial angle of a plastic deformation rate is related to the non-coaxial angle of a stress rate by use of strain rate sensitivity. Furthermore, a finite element analysis is carried out for a plane strain tension of homopolymer. Some remarkable numerical results of strain localization for homopolymer are discussed in detail.

Addendum to “Nonlinear quantum evolution with maximal entropy production”

The author calls attention to previous work with related results, which has escaped scrutiny before the publication of the article "Nonlinear quantum evolution with maximal entropy production", Phys.Rev.A63, 022105 (2001).

Nonlinear quantum evolution with maximal entropy production

We derive a well-behaved nonlinear extension of the nonrelativistic Liouville--von Neumann dynamics driven by maximal entropy production with conservation of energy and probability. The pure-state limit reduces to the usual Schr\"odinger evolution, while mixtures evolve toward maximum entropy equilibrium states with canonical-like probability distributions on energy eigenstates. The linear, near-equilibrium limit is found to amount to an essentially exponential relaxation to thermal equilibrium; a few elementary examples are given. In addition, the modified dynamics is invariant under the time-independent symmetry group of the Hamiltonian, and also invariant under the special Galilei group provided the conservation of total momentum is accounted for as well. Similar extensions can be generated for, e.g., nonextensive systems better described by a Tsallis q entropy.

Entropy Inequalities for Evaporation Condensation Problem in Rarefied Gas Dynamics

The present paper is devoted mainly to the half space problem for stationary Boltzmann-type equations. Using only conservation laws and the Boltzmann H-theorem we derive an inequality for unknown constant fluxes of mass, energy, and momentum. This inequality is expressed in terms of three parameters (pressure p, temperature T and the Mach number M) of the asymptotic Maxwellian at infinity. Geometrically the inequality describes a “physical” domain with positive entropy production in the 3-d space of the parameters. The domain appears to be qualitatively different for evaporation and condensation problems. We show that for given M, the curve p=p(M), T=T(M) of maximal entropy production practically coincides with the experimental evaporation curve obtained by Sone et al. on the basis of numerical solutions of BGK equation. Similar consideration for the condensation problem is also in qualitative agreement with known numerical results.

Thernromechanical Discussions on Constitutive Equations for Plastic Spin and Back Stress in a Theory of Dislocation Drift Rate.

A thermomechanical theory of elastoplasticity, including kinematic hardening at finite strain, is developed by introducing the concept of dislocation density tensor. The theory is self-consistent and is based on two fundamental principles, the principle of increase of entropy and the maximal entropy production rate. The thermomechanically consistent constitutive equations for plastic deformation rate, plasticspin and dislocation drift rate are rigorously derived. Constitutive equation of the plastic spin is directly obtained by taking account of a work associating with plastic spin and deriving stress. An expression for the back stress is given as a balance equation expressing equilibrium between internal stress and microstress conjugate to the dislocation density tensor. Moreover, it is shown that the present theory is sufficiently consistent with the theory of non-Riemannian plasticity.

A Thermodynamical Theory of Plastic Spin and Internal Stress With Dislocation Density Tensor

A thermodynamical theory of elastoplasticity including kinematic hardening and dislocation density tensor is developed. The theory is self-consistent and is based on two fundamental principles of thermodynamics, i.e., the principle of increase of entropy and maximal entropy production rate. The thermodynamically consistent governing equations of plastic spin and back stress are rigorously derived. An expression for the plastic spin tensor is obtained from the constitutive equation of dislocation drift rate tensor and an expression for the back stress tensor is given as a balance equation expressing an equilibrium between internal stress and microstress conjugate to the dislocation density tensor. Moreover, it is shown that, in order to obtain a thermodynamically consistent theory for kinematic hardening, the free energy density should have the dislocation density tensor as one of its arguments.

A thermodynamical theory of gradient elastoplasticity with dislocation density tensor. I: Fundamentals

A thermodynamical theory of gradient elastoplasticity, including kinematic hardening, is developed by introducing the concept of dislocation density tensor. The theory is self-consistent and is based on two fundamental principles, the principle of increase of entropy and the maximal entropy production rate. Thermodynamically consistent constitutive equations for plastic stretching, plastic spin and back stress are rigorously derived. Also, an expression for the plastic spin is obtained from the constitutive equation of dislocation drift rate and an expression for the back stress is given as a balance equation expressing equilibrium between internal stress and microstress conjugate to the dislocation density tensor. Moreover, it is shown that the present gradient theory yields a symmetric stress tensor. Some generalities and utility of this theory are discussed and comparisons with other gradient theories are given.

Thermomechanical Derivation of Noncoaxial Plastic Constitutive Equations Considering Spins of Objective Stress Rates.

Elasto-plastic constitutive equations which take into account yield-vertex effects are important in the study of localization instabilities of plastic deformations. However, they have never been discussed thermomechanically. In this paper, a method of deriving the above equations is proposed which is based on the second law of thermodynamics and the principle of maximal entropy production rate. Elastic strain as a strain measure which is conjugate to the objective stress rate is separated from total strain so that the Clausius-Duhem inequality, in which the Gibbs function is introduced as an elastic potential, can be always satisfied. The strain rate and stress rate are expressed by the same objective rate in the rate form of the elastic constitutive equation obtained. The plastic constitutive equation is derived using the principle of maximal dissipation rate. Since this equation is regarded as a flow rule in which the complementary dissipation function assumes the role of a plastic potential, it is indicated that the yield-vertex can exist on the dissipation surface. Furthermore, the spin which should be used in the objective stress rate is selected by taking into account not only usual requirements but also thermomechanical ones.

Thermomechanical Derivation of Noncoaxial Plastic Constitutive Equations Considering Spins of Objective Stress Rates.

Elastoplastic constitutive equations which take into account yield vertex effects are important in the study of localization instabilities of plastic deformations. However, they have never been discussed thermomechanically. In the present paper, a method of deriving the above equations is proposed which is based on the second law of thermodynamics and the principle of maximal entropy production rate. Elastic strain as a strain measure which is conjugate to objective stress rate is separated from total strain so that the Clausius-Duhem inequality, in which the Gibbs function is introduced as an elastic potential, can be always satisfied. The strain rate and stress rate are expressed by the same objective rate in the rate form of the elastic constitutive equation obtained. The plastic constitutive equation is derived using the principle of maximal dissipation rate. Since this equation is regarded as a flow rule in which the complementary dissipation function assumes the role of a plastic potential, it is indicated that the yield vertex can exist on the dissipation surface. Furthermore, the spin used in the objective stress rate is selected by taking into account not only conventional requirements but also thermomechanical ones.

Thermodynamics of Phase-Change Storage in Series With a Heat Engine

This paper addresses thermodynamics of phase-change storage elements in series with heat engines. It is assumed that the duration of the heat storage and the discharge are equal. It is also assumed that the same heat transfer fluid (HTF) with a constant flow rate is used for the whole cycle. The major constraint imposed on these systems is the stability of the temperature of the HTF supplied to the engine during the storage-discharge cycle. It is shown, for this setup, that the freezing point of the phase-change material (PCM) is defined by the First Law. Maximal stability corresponds to the freezing point equal to the arithmetic mean of the inlet temperatures of the hot and the cold streams. An analytic expression is developed for the Second Law efficiency of the heat storage-removal cycle for the phase-change element in series with an engine. It yields maximal entropy production in the absolute stability limit. Two analytically tractable models of a phase-change storage in series with a heat engine are studied in detail. One involves a PCM slab, and the second involves a PCM tube-and-shell heat exchanger.

On Master Operators with Extremal Entropy Production

Abstract The master operators B which cause the entropy production dH/dt = - k-1 dS/dt to become extremal for fixed statistical operators W are constructed and discussed. There are boundaries of the set B of master operators, B = {B | Σ B2 vu = b} for which the problem is solvable yielding minimal entropy production, while no solution exists in the set B without any constraints. Operators with maximal entropy production must be extremal points of B.