<![CDATA[<b>Flux Operators of Microdynamical Quantities in a Nonequilibrium Statistical Ensemble Formalism</b>]]>

Abstract

It is shown how the closure condition for the set of kinetic equations in Zubarev's Nonequilibrium Statistical Operator Method introduces a series of uxes of a reference set of densities. These uxes are the average values, over a Gibbs-like nonequilibrium generalized grandcanonical ensemble, of Hermitian operators for uxes de ned at the microscopic-mechanical level. The equations of evolution for these uxes or equivalently for their conjugated Lagrange multipliers are described.

Thermodynamic variables in the context of a nonequilibrium statistical ensemble approach

“…͑5͒ that the formalism introduces͔. But, as shown elsewhere, 3,37 the closure condition of Eq. ͑2͒ requires the introduction of the fluxes of these quantities 6,36,37 as basic variables, and with them all the other higher order fluxes ͑of tensorial rank rу2͒.…”

“…where I j is interpreted as the flux of quantity Q j , 36,37 and j accounts for sources and/or sinks of such a quantity. Making use of is Eq.…”

Informational Statistical Thermodynamics and Thermal Laser Stereolithography

“…The latter is based on the construction of the equations of evolution for the two basic densities, namely, that of particles, n(r, i), and that of energy, e(j%t), and their fluxes of all orders, namely, the two vectorial ones, f n (r,i) and / å (ú%ß), and the tensorial ones, /J|"'(r,i) and I^(r,t) (where r = 2> 3,... indicates tensorial rank and also the order of the flux): This is described in detail in [26], see also [27][28][29][30][31][32][33]. These hydrodynamic fields are the average over the nonequilibrium ensemble of a corresponding set of dynamical variables that the closure procedure of equation (2) introduces [26].…”

“…This is accomplished by writing all other quantities in terms of them, when calculating the average values with the use of the distribution of equation (11). This is described elsewhere [26][27][28][29][30][31][32][33] for several cases. For our purpose here, suffice it to say that, typically, the equations of evolution take the form…”

“…Moreover, in regime (II) we approximately obtain that (25) -i « and in regime (I) we write (26) with cu£ being a real frequency. Therefore, we can write equation (21) Equation (30) clearly tells us that the movement, as already noticed, is composed of a diffusive motion associated to the modes of long wavelengths, and damped undulatory motion associated to the modes with intermediate to short wavelengths, similarly -as it should -to the case of the telegrapher's equation in electrodynamics [38].…”