Macroscopic laws, microscopic dynamics, time's arrow and Boltzmann's entropy

Joel L. Lebowitz

Physica A: Statistical Mechanics and its Applications, 1993, vol. 194, issue 1, 1-27

Abstract: I discuss Boltzmann's resolution of the apparent paradox: microscopic dynamics are time-symmetric but the behavior of macroscopic objects, composed of microscopic constituents, is time-asymmetric. Noting the great disparity between macroscales and microscales Boltzmann developed a statistical approach which explains the observed macroscopic behavior. In particular it predicts the increase with time of the “Boltzmann entropy”, SB(X), for “almost all” microscopic states X, of a nonequilibrium macroscopic system. The quantitative description of the macroscopic evolution, and ipso facto the compatibility between the macroscopic descriptions and microscopic descriptions, is illustrated by an example: the rigorous derivation of a diffusion equation for the typical macroscopic density profile of a Lorentz gas of independent electrons moving according to Hamiltonian dynamics. The role of low entropy “initial states” is emphasized.

Date: 1993
References: View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0378437193903363
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:194:y:1993:i:1:p:1-27

DOI: 10.1016/0378-4371(93)90336-3

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 ().