Response to “comments on Keizer's critique on extended irreversible thermodynamics” by B. C. Eu

Journal of Statistical Physics -     

On the relationship between fluctuating irreversible thermodynamics and “extended” irreversible thermodynamics

The relationship between fluctuating irreversible thermodynamics and theories of irreversible processes which include the thermodynamic fluxes as independent variables is explored. It is shown that the usual fluctuating linear theory of irreversible thermodynamics is a contraction of the extended theory. This contraction contains non-Markovian effects dependent upon the relaxation times associated with the thermodynamic fluxes. In the limit that these relaxation times are small, the extended theory is shown to be equivalent to the usual fluctuating thermodynamic theory. A critique of the extended theories is given from the point of view of the mechanistic statistical theory of irreversible processes.     

Further comments on the modified operator method

It is shown that a recently proposed perturbation approach to the two-step coherent-state approximation for one-dimensional oscillators leads to series which are asymptotically divergent, and coincident with the ones derived from the operator method. A simple method is provided to transform such a series into a convergent renormalized one making use of an order-dependent mapping. Results are excellent for all eigenvalues and all coupling constants.     

Response to comments

The author affirms the previous position and responds to specific comments raised by Cahn in the preceding article.     

Concepts of stability and symmetry in irreversible thermodynamics. I

Concepts of stability and symmetry in irreversible thermodynamics are developed through the analysis of system energy flows. The excess power function, derived from a local energy conservation equation, is shown to yield necessary and sufficient stability criteria for linear and nonlinear irreversible processes. In the absence of symmetry-destroying external forces, the linear range may be characterized by a set of phenomenological coefficient symmetries relating coupled forces and displacements, velocities, and accelerations, whereas rotational phenomena in nonlinear processes may be characterized by skew-symmetric components of the phenomenological coefficients. A physical interpretation of the nature of the skew-symmetric parts is given and the variational principle of minimum dissipation of energy is related to a stability criterion.     

The application of the thermodynamics of irreversible processes to welding arcs

The self-regulation of an inert gas shielded metal welding arc is dealt with briefly. A thermodynamic equation is derived for the self-regulation of such an arc.

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Some comments on the thermodynamics of sonoluminescence--a personal view

The path of the gas in a sonoluminescent bubble must enclose an area in a P-V plot if the gas itself emits photons. Thermodynamic analysis thus delineates the playing field that may enable us to distinguish liquid-phase emissions from gas-phase emissions. The apparent importance of the van der Waals a (which parameterizes mean-square induced dipole attractions) in light intensity supports collision-induced emission as a likely mechanism. The suggested emitting object, containing 10(10) molecules in picosecond-long van der Waals contact, is novel, being neither plasma, gas, liquid nor blackbody. The bubble pursues a unique thermodynamic path.     

Kinetic theory of dense fluids. IV. Entropy balance equation and irreversible thermodynamics

The viscosity coefficient obtained in a previous paper of this series is calculated as a function of density by developing the N-particle collision operator into a dynamic cluster expansion. The excess transport coefficient Δη is given in an exponential form, where η₀ is the two-body Chapman-Enskog result for the transport coefficient, n is the density, and β_l is a density-independent quantity consisting of connected cluster contributions of (l + 2) particles. Therefore, the leading term β₁ consists of connected three-body cluster contributions. The excess shear viscosity coefficient is calculated for a monatomic hard-sphere fluid by computing β_l up to the three-body contributions and the result is compared with the molecular dynamics result by Ashurst and Hoover and also with the experimental data on Ar at 75°C. In spite of the crudity of the potential model used and the approximations made the agreement is good. The result can be improved if l-body clusters (l 4) are included in the calculation. The thermal conductivity coefficient can be obtained in a similar form by using exactly the same procedure used for the viscosity coefficient.     

Response to comments on boundary problems and electromagnetic constitutive parameters

The positive conclusion on the recognizable existence of the Tellegen parameter, which invalidates the Post constraint, arrived at in the Comment of Sihvola and Tretyakov through the solution of a boundary-value problem relies on a framework of macroscopic electromagnetism that lacks a microscopic basis. But the microscopic viewpoint underlying the framework of modern macroscopic electromagnetism invalidates the boundary conditions used therein, and instead validates the Post constraint.     

Comparison of and comments on two thermodynamic approaches (reversible and irreversible) to ferroelectric phase transitions

In this article, we compared and commented on two thermodynamic approaches, i.e. the reversible and irreversible ones to ferroelectric phase transitions especially in the case of first-order. The reversible approach, otherwise known as the Landau–Devonshire theory proved not to possess a firm physical basis according to the concepts and methods originating from the field theory and those originating from the analytical dynamics. The metastable states hypothesis underlying the Landau–Devonshire theory causes an unpleasant consequence and a logical conflict. As for the new-developed irreversible approach, we demonstrated that the fundamental hypothesis of stationary states underlying it, is reliable with the aid of non-equilibrium variational principles. The difficulties encountered within the Landau–Devonshire theory can be overcome while this approach is applied to the first-order ferroelectric phase transitions. There is some justification made to prove the proposition.     

On the definitions of entropy and temperature in the extended thermodynamics of irreversible processes

New definitions of entropy and temperature for uniform systems that fast exchange heat with the environment are considered. Instead of the known local equilibrium hypothesis, a local uniformity hypothesis is proposed. Within the proposed formalism of extended thermodynamics of irreversible processes, dual-phase-lag transfer equations are obtained. To cite this article: S.I. Serdyukov, C. R. Physique 8 (2007).     

A reply to the comments of Johnson et al. on the thermodynamics of the Heisenberg-Ising ring for |Δ|<1

An improved set of integral equations for the thermodynamics of the Heisenberg-Ising chain for |Δ|<1 is given under some new assumptions. This yields the high-temperature expansion of the free energy correctly, at least, up to the second term.