Statistical mechanical foundations for systems with nonexponential distributions

Traditionally the exponential canonical distributions of Gibbsian statistic al mechanics are given theoretical justification in at least four different ways: steepest descent method, counting method, Khinchin's method based on the central limit theorem, and maximum entropy principle of Jaynes. Equall y ubiquitous power-law canonical distributions are shown to be given simila r justification by appropriately adopting these formulations. (C) 2001 Else vier Science Ltd. All rights reserved.