The Einstein-Smoluchowski promeasure versus the Boltzmann(-Peierls) equation

Zbigniew Banach and Sławomir Piekarski

Physica A: Statistical Mechanics and its Applications, 1992, vol. 180, issue 3, 336-358

Abstract: Beginning from the specific model of the Boltzmann-Peierls equation for the distribution function f(k, t), the time-dependent theory of fluctuations is developed from Einstein's inversion of Boltzmann's relation. The distribution function f(k, t) that satisfies the Boltzmann-Peierls equation is to be viewed as a random variable characterizing the macro-state of a gas of quasiparticles (phonons, magnons, rotons, etc.). The crucial assumption entering into the present approach is simply that the randomness in the statistical distribution of the initial values of f(k, t) can be characterized by the Einstein-Smoluchowski promeasure μϵ. It is convenient to think of μϵ as being the infinite-dimensional analog of Einstein's distribution law in the Gaussian approximation. The equilibrium promeasure μϵ is used to study the correlations in time of fluctuations in the moments of f(k, t). Some problems associated with a kinetic version of the Green-Kubo approach to transport processes are carefully studied. The exact formula for the thermal conductivity coefficient ϰT, which is derived in this paper, emerges as a portion of the general formalism.

Date: 1992
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0378437192903946
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:180:y:1992:i:3:p:336-358

DOI: 10.1016/0378-4371(92)90394-6

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().