L E Beghian and E Sheldon 2001 J. Phys. A: Math. Gen. 34 2913 doi:10.1088/0305-4470/34/14/301
L E Beghian1,2 and E Sheldon2
Show affiliationsAn alternative interpretation to Gibbs' concept of the canonical distribution for an ensemble of systems in statistical equilibrium is proposed. Whereas Gibbs' theory is based upon a consideration of systems subject to dynamical law, the present analysis relies neither on the classical equations of motion nor makes use of any a priori probability of a complexion; rather, it makes avail of the basic algebra of random variables and, specifically, invokes the law of large numbers. Thereby, a canonical distribution is derived which describes a macrosystem in probabilistic, rather than deterministic, terms, and facilitates the understanding of energy fluctuations which occur in macrosystems at an overall constant ensemble temperature. A discussion is given of a modified form of the Gibbs canonical distribution which takes full account of the effects of random energy fluctuations. It is demonstrated that the results from this modified analysis are entirely consonant with those derived from the random-variable approach.
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
Issue 14 (13 April 2001)
Received 22 August 2000, in final form 12 January 2001
L E Beghian and E Sheldon 2001 J. Phys. A: Math. Gen. 34 2913
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