Uniformity of the phase space and fluctuations in thermal equilibrium

Details Uniformity of the phase space and fluctuations in thermal equilibrium Uniformity of the phase space and fluctuations in thermal equilibrium

2002-11-04

arxiv.org/abs/cond-mat/0211061v1

Physica A 322C(2003)313-328

Physics

Condensed Matter

Statistical Mechanics

20 pages, 20 figures

Scientific paper

10.1016/S0378-4371(02)01814-9

General relations are found between the measure of the uniformity of distributions on the phase space and the first moments and correlations of extensive variables for systems close to thermal equilibrium. The role played by the parameter of the Renyi entropy for the analysis of their fluctuations and correlations is studied. Analytical results are verified and illustrated by direct simulations of quantum systems of ideal fermions and bosons. Problems of finite statistics, usual in experiments and simulations, are addressed and discussed and solved by finding unbiased estimators for Renyi entropies and uniformities.

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